Model Assumptions Research Articles

Euclid and KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear analyses

Cosmic shear is a powerful probe of cosmological models and the transition from current Stage-III surveys such as the Kilo-Degree Survey (KiDS) to the increased area and redshift range of Stage IV surveys such as will significantly increase the precision of weak lensing analyses. However, with increasing precision, the accuracy of model assumptions needs to be evaluated. In this study, we quantify the impact of the correlated clustering of weak lensing source galaxies with the surrounding large-scale structure, known as source-lens clustering (SLC), which is commonly neglected. We include the impact of realistic scatter in photometric redshift estimates, which impacts the assignment of galaxies to tomographic bins and increases the SLC . For this, we use simulated cosmological datasets with realistically distributed galaxies and measure shear correlation functions for both clustered and uniformly distributed source galaxies. Cosmological analyses are performed for both scenarios to quantify the impact of SLC on parameter inference for a KiDS-like and a setting. We find for Stage III surveys such as KiDS, SLC has a minor impact when accounting for nuisance parameters for intrinsic alignments and shifts of tomographic bins, as these nuisance parameters absorb the effect of SLC, thus changing their original meaning. For KiDS ( the inferred intrinsic alignment amplitude $A_ IA $ changes from $0.11_ $) for data without SLC to $0.28_ $) with SLC. However, fixed nuisance parameters lead to shifts in $S_8$ and $ m $, emphasizing the need for including SLC in the modelling. For we find that $ m $, and $w_0$ are shifted by 0.19, 0.12, and 0.12 sigma , respectively when including free nuisance parameters and by 0.20, 0.16, and 0.32 sigma when fixing the nuisance parameters. Consequently, SLC on its own has only a small impact on the inferred parameter inference when using uninformative priors for nuisance parameters. However, SLC might conspire with the breakdown of other modelling assumptions, such as magnification bias or source obscuration, which could collectively exert a more pronounced effect on inferred parameters.

Viscosity of aqueous ammonium nitrate–organic particles: equilibrium partitioning may be a reasonable assumption for most tropospheric conditions

Abstract. The viscosity of aerosol particles determines the critical mixing time of gas–particle partitioning of volatile compounds in the atmosphere. The partitioning of the semi-volatile ammonium nitrate (NH4NO3) might alter the viscosity of highly viscous secondary organic aerosol particles during their lifetimes. In contrast to the viscosity of organic particles, data on the viscosity of internally mixed inorganic–organic aerosol particles are scarce. We determined the viscosity of an aqueous ternary inorganic–organic system consisting of NH4NO3 and a proxy compound for a highly viscous organic, sucrose. Three techniques were applied to cover the atmospherically relevant humidity range: viscometry, fluorescence recovery after photobleaching, and the poke-flow technique. We show that the viscosity of NH4NO3–sucrose–H2O with an organic to inorganic dry mass ratio of 4:1 is 4 orders of magnitude lower than the viscosity of the aqueous sucrose under low-humidity conditions (30 % relative humidity (RH), 293 K). By comparing viscosity predictions of mixing rules with those of the Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients Viscosity (AIOMFAC-VISC) model, we found that a mixing rule based on mole fractions performs similarly when data from corresponding binary aqueous subsystems are available. Applying this mixing rule, we estimated the characteristic internal mixing time of aerosol particles, indicating significantly faster mixing for inorganic–organic mixtures compared to electrolyte-free particles, especially at lower RH. Hence, the assumption in global atmospheric chemistry models of quasi-instantaneous equilibrium gas–particle partitioning is reasonable for internally mixed single-phase particles containing dissolved electrolytes (but not necessarily for phase-separated particles), for most conditions in the planetary boundary layer. Further data are needed to see whether this assumption holds for the entire troposphere at midlatitudes and at RH > 35 %.

Do rising interest rates matter for bank profitability? Evidence from Portuguese banks

The purpose of this paper is to analyse the profitability determinants of seventeen banks operating in Portugal from 2013 to 2023. The banking market has changed significantly, particularly since 2021, when Euribor grew rapidly to control inflation target. Methodologically, a hypothetical-deductive approach was used based on panel data collected from banks' published accounts. To generate results, grouped ordinary least squares were applied, as the Breusch-Pagan test confirms homoscedasticity, an essential assumption in this regression model. Internal variables considered include credit quality, capital adequacy, management quality, financial margin, and bank size, alongside an external variable, the Euribor. The findings reveal that credit risk, capital adequacy, management capacity, and Euribor are the most statistically significant for both return on equity and return on assets, with Euribor emerging as the greatest statistically significant variable. The analysis of Euribor as an explanatory variable represents the key contribution of this study relative to the existing and reviewed literature.

Determination of solid-liquid adhesion work on flat surfaces in a direct and absolute manner

There is a long-standing need for a direct determination of solid-liquid work of adhesion due to its central role in several scientific and industrial fields. Here, a method is introduced to determine the value of adhesion work on flat surfaces directly, without the need of any model assumptions, and independently from uncertainties of contact angles. The presented method enables to determine the adhesion work separately both for advancing and receding situations. The directly measured adhesion work values were benchmarked successfully against the prediction of the Young–Dupré equation in the 0°–120° contact angle range. That is, the Young–Dupré equation was experimentally proven to be valid separately for both advancing and receding cases. The method provides an absolute, thermodynamic quantity, hence it is insensitive to the measurement parameters, moreover the resulting values can be used directly in further calculations.

Learning in Associative Networks Through Pavlovian Dynamics

Abstract Hebbian learning theory is rooted in Pavlov’s classical conditioning While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently has it been numerically shown that it is possible to write neural and synaptic dynamics that mirror Pavlov conditioning mechanisms and also give rise to synaptic weights that correspond to the Hebbian learning rule. In this letter we show that the same dynamics can be derived with equilibrium statistical mechanics tools and basic and motivated modeling assumptions. Then we show how to study the resulting system of coupled stochastic differential equations assuming the reasonable separation of neural and synaptic timescale. In particular, we analytically demonstrate that this synaptic evolution converges to the Hebbian learning rule in various settings and compute the variance of the stochastic process. Finally, drawing from evidence on pure memory reinforcement during sleep stages, we show how the proposed model can simulate neural networks that undergo sleep-associated memory consolidation processes, thereby proving the compatibility of Pavlovian learning with dreaming mechanisms.

Smoothed Estimation on Optimal Treatment Regime Under Semisupervised Setting in Randomized Trials.

A treatment regime refers to the process of assigning the most suitable treatment to a patient based on their observed information. However, prevailing research on treatment regimes predominantly relies on labeled data, which may lead to the omission of valuable information contained within unlabeled data, such as historical records and healthcare databases. Current semisupervised works for deriving optimal treatment regimes either rely on model assumptions or struggle with high computational burdens for even moderate-dimensional covariates. To address this concern, we propose a semisupervised framework that operates within a model-free context to estimate the optimal treatment regime by leveraging the abundant unlabeled data. Our proposed approach encompasses three key steps. First, we employ a single-index model to achieve dimension reduction, followed by kernel regression to impute the missing outcomes in the unlabeled data. Second, we propose various forms of semisupervised value functions based on the imputed values, incorporating both labeled and unlabeled data components. Lastly, the optimal treatment regimes are derived by maximizing the semisupervised value functions. We establish the consistency and asymptotic normality of the estimators proposed in our framework. Furthermore, we introduce a perturbation resampling procedure to estimate the asymptotic variance. Simulations confirm the advantageous properties of incorporating unlabeled data in the estimation for optimal treatment regimes. A practical data example is also provided to illustrate the application of our methodology. This work is rooted in the framework of randomized trials, with additional discussions extending to observationalstudies.

Effect of powder and absorptivity assumptions in the high-fidelity modeling of Laser Powder Bed Fusion processes

Laser Powder Bed Fusion (LPBF) technology represents the most promising metal additive manufacturing process to be scaled up to an industrial level for producing full batches of parts within the automotive aerospace and health sectors, among others. Despite this higher technological readiness, imperfections such as warping, porosities or undesired non-equilibrium microstructures can arise unexpectedly due to the complex thermal histories inherent to LPBF. Being able to anticipate to such imperfections is thus of high importance. With this purpose, numerical modeling strategies can be employed to significantly reduce experimental work on the melt pool scale. This allows to quantify the odds and magnitude of these process unwanted effects. More precisely, Computational Fluid Dynamics (CFD) enables high-fidelity models on the laser-matter interaction during LPBF processing. In this work, a modeling approach is presented in which the driving forces for melt formation are included in a CFD workspace, where multiple reflections of the laser on the melt pool Liquid-Gas Interface (LGI) are considered by means of an absorptivity function of the LGI depth. This simplification and the use of adaptive mesh strategies allows the model to be computed within a reasonable time. Results and applicability of the model on the determination of the melting mode (conduction or keyhole) are displayed and compared with experimental measurements of the melt pool width and depth for 316L and Ti64 single tracks produced on a LPBF machine. Likewise, further aspects such as total absorbed power are assessed.

Towards Effective Clustered Federated Learning: A Peer-to-Peer Framework With Adaptive Neighbor Matching

In federated learning (FL), clients may have diverse objectives, and merging all clients' knowledge into one global model will cause negative transfer to local performance. Thus, clustered FL is proposed to group similar clients into clusters and maintain several global models. In the literature, centralized clustered FL algorithms require the assumption of the number of clusters and hence are not effective enough to explore the latent relationships among clients. In this paper, without assuming the number of clusters, we propose a peer-to-peer (P2P) FL algorithm named PANM. In PANM, clients communicate with peers to adaptively form an effective clustered topology. Specifically, we present two novel metrics for measuring client similarity and a two-stage neighbor matching algorithm based Monte Carlo method and Expectation Maximization under the Gaussian Mixture Model assumption. We have conducted theoretical analyses of PANM on the probability of neighbor estimation and the error gap to the clustered optimum. We have also implemented extensive experiments under both synthetic and real-world clustered heterogeneity. Theoretical analysis and empirical experiments show that the proposed algorithm is superior to the P2P FL counterparts, and it achieves better performance than the centralized cluster FL method. PANM is effective even under extremely low communication budgets.

The Information Value of Geographical Indications

We conduct laboratory experiments in Spain (N = 148) and France (N = 143) simulating a wine shopping experience in which participants choose between four wines in a limited information environment, and access to Geographical Indication (GI) information, winery names, and expert review scores are “purchased” in multiple price listing elicitation sessions. Data analysis leverages the sequential nature of the rounds, experimental treatments, and a wine knowledge questionnaire to investigate the hierarchical structure and level of redundancy between alternative information sources, the role played by wine prices, and previously acquired expertise. We estimate that the average value of accessing GI information in a pre-purchase scenario lies between EUR 0.33 (Spain) and EUR 0.37 (France) for each purchasing occasion, and expert reviews provide a similar level of information. These findings are consistent across different price segments (high: €13-€17 vs. low: €4-€7). Firm names have lower average valuation but are more useful to high-knowledge consumers. GIs, firm names, and expert reviews are found to be imperfect substitutes, suggesting that GIs capture elements of both horizontal and vertical differentiation. The discussion is structured along three main thematic areas of contribution: the role of GIs as signals of quality, the extant literature studying how consumers interpret quality signals, and the contrast between our findings and the modeling assumption adopted in the GI theoretical literature.

Comparative assessment of airborne infection risk tools in enclosed spaces: Implications for disease control

The COVID-19 pandemic, caused by SARS-CoV-2, highlighted the importance of understanding transmission modes and implementing effective mitigation strategies. Recognizing airborne transmission as a primary route has reshaped public health measures, emphasizing the need to optimize indoor environments to reduce risks. Numerous tools have emerged to assess airborne infection risks in enclosed spaces, providing valuable resources for public health authorities, researchers, and the general public.However, comparing the outputs of these tools is challenging because of variations in assumptions, mathematical models, and data sources. We conducted a comprehensive review, comparing digital airborne infection risk calculators using standardized building-specific input parameters. These tools generally produce similar and consistent outputs with identical inputs. Variations mainly stem from model selection and the handling of unsteady viral load conditions. Differences in source term calculations, including particle emission concentrations and respiratory activity, also contribute to disparities. These differences are minor compared to the inherent uncertainties in risk assessment. Consistency in results increases with higher ventilation rates, showing a robust trend across models. However, inconsistencies arose in the inclusion of face masks, often due to the lack of detailed efficiency values. Despite some differences, the overall consistency underscores the value of these tools in public health strategy and infectious disease control.We also compared some of the model's efforts to conduct retrospective assessments against reported transmission events by assuming input parameters to the models so that the calculated risk would closely fit the original outbreak infection rate. Thus, validating these models against past outbreaks remains challenging because of the lack of essential input information from observed events. This comparative analysis demonstrates the importance of transparent data sources and justifiable model assumptions to enhance the reliability and precision of risk assessments.

Gradient-induced variable selection in reproducing kernel Hilbert space for survival analysis

The analysis of survival data is often hampered by a potentially very large number of covariates compounded with incomplete data. This paper considers the problem of variable selection where the response is subject to random (right) censoring. We introduce a model-free variable selection procedure via learning the gradients of quantile regression functions with two popular censoring weighting schemes. The key advantage of the proposed approach is that it does not require explicit model assumptions and is computationally efficient. Besides, we also prove its asymptotic consistency and examine its finite sample performance via numerical studies. As an empirical example, the proposed procedure is applied for the analysis of a breast cancer data set.

Black hole-black hole mergers with and without an electromagnetic counterpart: A model for stable tertiary mass transfer in hierarchical triple systems

Triple stars are prevalent within the population of observed stars. Their evolution compared to binary systems is notably more complex and is influenced by unique dynamical, tidal, and mass transfer processes inherent in higher order multiples. Understanding these phenomena is essential for comprehensive insight into multistar evolution and the formation of energetic transients, including gravitational wave (GW) mergers. Our study aims to probe the evolution of triple star systems when the tertiary component fills its Roche lobe and transfers mass to the inner binary. Specifically, we focus on the impact of tertiary mass transfer on the evolution of the inner orbit and investigate whether it could lead to the formation of GW sources with distinct properties. To achieve this, we developed an analytical model that describes the evolution of the inner and outer orbits of hierarchical triples undergoing stable mass transfer from the tertiary component. We have publicly released this model as a python package on Zenodo. Utilising population synthesis simulations, we investigated triples with a Roche-lobe filling tertiary star and an inner binary black hole (BBH). These systems stem from inner binaries experiencing chemically homogeneous evolution (CHE). Our analysis encompasses two distinct populations with metallicities of $Z=0.005$ and $Z=0.0005$, focusing on primary components in the inner binary with initial masses ranging from 20 to $100\ M odot $ and inner and outer orbital separations of up to $40\ R odot $ and $10^5\ R odot $, respectively, targeting the parameter space where chemically homogeneous evolution is anticipated. Our results indicate that for the systems we studied, the mass transfer phase predominantly leads to orbital shrinkage of the inner binary and evolution towards non-zero eccentricities and is accompanied by an expansion of the outer orbit. In the systems where the inner binary components evolve in a chemically homogeneous manner, 9.5<!PCT!> result in mass transfer from the tertiary onto an inner BBH. Within this subset, we predict a high formation efficiency of GW mergers ranging from 85.1<!PCT!> to 100<!PCT!> at $Z=0.005$ and 100<!PCT!> at $Z=0.0005$ with short delay times, partly attributable to the mass transfer phase. Owing to the rarity of triples with a CHE inner binary in the stellar population, we project local merger rates in the range of 0.69 to 1.74 $ Gpc^ $. Of the prospected BBH mergers that enter the LISA and aLIGO frequency band due to GW emission, a fraction is still accreting gas from the tertiary star. This could produce a strong electromagnetic (EM) counterpart to the GW source and maintain high eccentricities as the system enters the frequency range detectable by GW detectors. The occurrence of EM signals accompanying mergers varies significantly depending on model assumptions, with fractions ranging from less than 0.03<!PCT!> to as high as 46.8<!PCT!> of all mergers if the formation of a circumbinary disc is allowed.

Digitalization and Sustainability of Supply Chains: Assessing the Potential of the DYLLI Application in the Hotel, Restaurant, and Catering Industry

This article investigates the integration of Information and Communication Technologies (ICT) to enhance service quality and sustainability within the Hotel, Restaurant, and Catering (HoReCa) sector. The study aims to explore how improved communication through ICT can optimize supply chain processes and elevate service standards. A usability analysis was conducted via surveys among HoReCa companies to assess perceptions of a demo application designed to facilitate sustainable practices. Additionally, a competitiveness analysis, grounded in Porter’s Five Forces model, examines the dynamics of mobile applications in the HoReCa market. The usability analysis validates business model assumptions while providing insights into market challenges and opportunities. The findings indicate that volatile commodity prices and recruitment difficulties are significant challenges for restaurateurs, highlighting the need for tools that support sustainable operations. The proposed ICT solutions serve as innovative tools that improve communication between HoReCa businesses and their suppliers, thereby directly influencing service quality. By promoting transparency in pricing and collaboration terms, these solutions align with sustainable supply chain principles, addressing environmental concerns while meeting evolving consumer expectations. This research contributes to the literature on competitiveness in the HoReCa sector by emphasizing the pivotal role of technology in fostering both service quality and sustainable development.

Ridgecrest Aftershock Stress Drops from P- and S-Wave Spectral Decomposition

ABSTRACT Seismic moment and stress drop are crucial for understanding earthquake rupture processes, but their estimates often have large uncertainties for small earthquakes. Stress drop is typically inferred from an earthquake’s source spectrum based on theoretical models, but poorly constrained path corrections and other modeling assumptions limit the accuracy of stress-drop estimates. Here, we compute stress drops using both P and S waves for the 2019 Ridgecrest earthquake sequence, compare their estimates, and evaluate the associated uncertainties. We use spectral decomposition and apply the analysis to both types of waves for the same set of earthquakes, adjusting some S-wave parameter choices to obtain overall consistency with our P-wave results. Our approach fixes the corner frequency of small calibration earthquakes to reduce scatter in the estimated source parameters of the larger earthquakes. We find that assuming a lower high-frequency fall-off rate for S waves yields more consistent absolute stress-drop estimates between P and S waves. Our stress-drop estimates appear to increase slightly with magnitude for earthquakes with magnitudes >∼3.4. Furthermore, we find that the stress-drop estimates using both types of data exhibit coherent spatial variations. Earthquakes near the Coso geothermal field tend to have lower stress drops, and earthquakes near the M 7.1 hypocenter have higher stress-drop estimates. This spatial pattern is consistently observed in both the P- and S-wave results. We find no strong correlation between our stress-drop estimates and the M 7.1 Ridgecrest earthquake slip distribution, suggesting a heterogeneous stress environment for the Ridgecrest fault system.

Latent class choice models with an error structure: Investigating potential unobserved associations between latent segmentation and behavior generation

Latent class choice modeling has gained great popularity in the transportation and choice modeling communities across the years. However, discussion of principles associated with the specification of the class membership model has barely appeared in the literature. Related to this issue, this study questions whether one of the basic assumptions of latent class choice modeling, that of independence between latent segmentation and the behavior generation process, is tenable. We formulate latent class choice models where the unobserved influences on latent segmentation and behavior generation are correlated, by introducing an error structure reflecting that supposition. The proposed method is applied to two empirical settings. In the first application, the dependent variable is an ordinal variable measuring willingness to share autonomous vehicle rides with strangers. In the second application, the dependent variable is a binary indicator of whether a person has used ridehailing services for social purposes. In both applications, error correlations were statistically significant, indicating that the segmentation and behavior generation processes are jointly determined. Although goodness of fits and parameter estimates per se are similar to those of the standard latent class choice models for these particular applications, allowing an error structure leads to a subtle change in model implications. In particular, our scenario analyses, which present marginal effects, illustrate the value of the proposed model for considering jointness arising from correlated errors, in contrast to standard latent class models. Lastly, we propose several avenues for future research.

Test for conditional Poissonity in integer-valued conditional autoregressive models

The Poisson distribution is a representative distribution for discrete data, much like the normal distribution is for continuous data. Many time series models for count data have been developed based on the Poisson distribution. However, studies examining the validity of the Poisson assumption in these time series models have been relatively scarce. This study addresses the problem of testing for conditional Poissonity in integer-valued conditional autoregressive models. For this purpose, we introduce a test statistic based on the information matrix of the likelihood function. Under regularity conditions, it is shown that the proposed test has an asymptotic null distribution following a chi-square distribution. Simulation results demonstrate the validity of the proposed test. Additionally, a real data analysis is provided for illustration.

Predicting long-term tensile degradation of GFRP rebars embedded in concrete with a reconsidered environmental reduction factor [formula omitted]

Glass fiber reinforced polymer (GFRP) has been considered as an advanced material to replace conventional steel reinforcements in concrete structures to address the corrosion issue. The degradation of GFRP rebars, which may threaten both the durability and safety of infrastructures, is a major concern. To predict the 100-year strength retention of GFRP under various temperature and relative humidity conditions, the environmental reduction factor (CE) is applied in engineering. The conventional CE based on the assumption of logarithmic degradation model is commonly utilized during the degradation phase spanning from a few years to decades; however, it is not applicable to the initial and perpetual degradation phases. To address this issue, a novel environmental reduction factor (CE′) based on the exponential degradation model considering temperature and relative humidity is proposed in this study. Both CE and CE′ are mathematically deduced from empirical degradation data and then evaluated in a case study involving GFRP-concrete samples soaked in water at 23, 40 or 60 °C for up to 12 months within the authors’ dataset. Experimental results show that the GFRP tensile strength degradation is closer to the exponential model, reaching a plateau (47.4%) after 12-month exposure to 60 °C water. Moreover, the tensile strength retention of GFRP rebars in Vancouver (10 °C), Shanghai (16 °C) and Houston (22 °C) is predicted considering various scenarios of relative humidities (0–90%). Further research indicates that CE′ (0.65–0.78) exhibits a smaller value compared to CE (0.81) at a temperature of 22 °C and a relative humidity of 90% following a 100-year exposure period, thereby providing engineers with a more conservative design approach for GFRP in real-world scenarios. Nevertheless, this exponential degradation model requires a thorough consideration of severe degradation state during the extended aging period, which may not be applicable to GFRP structures exhibiting exceptional durability.

Transient Stability-Based Fast Power System Contingency Screening and Ranking

Today’s power systems are operated closer to their stability limits due to the continuously growing load demands, interface to open markets, and integration of more renewable energies. In order to provide operators with clear insight on the current system situation, near real-time power systems dynamic security assessment tools are required. One of the core elements of near real-time dynamic security assessment tools is contingency screening and ranking. Most of the commercially available tools screen and rank contingencies by using the traditional numerical integration or Transient Energy Functions (TEFs) or hybrid methods. The traditional numerical integration method is accurate but computationally intensive and has a slow assessment speed which makes it difficult to identify any insecure contingency before it happens. Despite the TEF method of transient stability analysis being relatively fast, it develops less accurate results due to models simplification and assumptions. This paper introduces transient stability based on fast and robust contingency screening and ranking using an Adaptive step-size Differential Transformation (AsDTM) method. Based on the most current snapshot from Supervisory Control and Data Accusation (SCADA) data, the proposed method triggers AsDTM-based transient stability simulation for each credible contingency and evaluates Transient Stability Indices (TSI) as the normalized weighted sum of squares of errors derived from state variables and complex bus voltages at every simulation time step. Finally, contingencies are ranked based on these TSI and the worst contingency is identified for the next detail assessment. The method is tested on IEEE 9 bus and 39 bus test systems. Test results reveal that the proposed method is faster, robust, and can be used in near real-time dynamic security assessment sessions.

Uniform in Number of Neighbor Consistency and Weak Convergence of k-Nearest Neighbor Single Index Conditional Processes and k-Nearest Neighbor Single Index Conditional U-Processes Involving Functional Mixing Data

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation r(m)(φ,t), defined as E[φ(Y1,…,Ym)|(X1,…,Xm)=t] for t∈Xm. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems.

Model-based optimal randomization procedure for treatment-covariate interaction tests.

Linear models are extensively used in the analysis of clinical trials. However, required model assumptions (e.g. homoscedasticity) may not be satisfied in practice, resulting in low power of treatment-covariate interaction tests. Various interaction tests have been proposed to improve the efficiency of detecting differences in treatment-covariate interactions. Aiming to fundamentally improve the power of treatment-covariate interaction tests, for heteroscedasticity of treatment responses, we develop a model-based optimal randomization procedure, referred to as model-based Neyman allocation (MNA) in this article. Thederived limiting allocation proportion indicates that the procedure MNA is a generalization of response-adaptive randomization targeting Neyman allocation (RAR-NA). In theory, we demonstrate that the procedure MNA can maximize the power of treatment-covariate interaction tests. The issue of sample size estimation is also addressed. Simulation studies show, in the framework of the heteroscedastic linear model, compared with Pocock and Simon's minimization method and RAR-NA, the procedure MNA has the greatest power of tests for both systematic effects and treatment-covariate interactions, even under model misspecification. Finally, the efficiency of the procedure MNA is illustrated by a hypothetical case study based on a real schizophrenia clinical trial.