Parameter Estimation Research Articles

The influence mechanism of internet finance on residents’ online consumption

This study investigates the impact of Internet finance (IF)11Internet finance (IF): Traditional financial institutions and Internet enterprises use Internet technology and information communication technology to realize the new financial business model of financial financing, payment, investment and information intermediary services.on residents’ online consumption using annual data from 2013 to 2022 in China. To examine the impact of IF on overall consumption, survival, development, and enjoyment, four vector autoregressive models are constructed. This study employs comprehensive methods, including parameter estimation, impulse response function analysis, and variance decomposition. Findings reveal that the development of IF has significantly stimulated residents’ online consumption, with the increase in developmental expenditure being the most significant, followed by the increase in entertainment expenditure.

Does sovereignty help economic growth? A recent reassessment

There is relevant literature that has found that independence harmed economic growth in some former colonies, but there are few to no systematic and recent empirical analyses on the relationship between sovereignty and economic growth. We follow and enhance the Solow–Swan growth model to measure economic convergence with the United States. This model was estimated through feasible generalized least squares panel regressions and robust regressions. These estimations allow us to capture the experience of recent (since the 1950s) sovereignties vis-à-vis long-existing countries and the economic outcomes of democratic sovereignties. We then stratify economies by region and income level and show propensity score matching estimators of recent former colonies with other countries that share similar growth determinants. On average, our parameter estimates suggest that independence causes countries’ per capita income to converge with that of the United States. Initial democratic and economic conditions appear to be among the modifying factors between sovereignty and economic growth.

The biogeochemical model Biome-BGCMuSo v6.2 provides plausible and accurate simulations of the carbon cycle in central European beech forests

Abstract. Process-based ecosystem models are increasingly important for predicting forest dynamics under future environmental conditions, which may encompass non-analogous climate coupled with unprecedented disturbance regimes. However, challenges persist due to the extensive number of model parameters, scarce calibration data, and trade-offs between the local precision and the applicability of the model over a wide range of environmental conditions. In this paper, we describe a protocol that allows a modeller to collect transferable ecosystem properties based on ecosystem characteristic criteria and to compile the parameters that need to be described in the field. We applied the procedure to develop a new parameterisation for European beech (Fagus sylvatica L.) for the Biome-BGCMuSo model, the most advanced member of the Biome-BGC family. For model calibration and testing, we utilised multiyear forest carbon data from 87 plots distributed across five European countries. The initial values of 48 new ecophysiological parameters were defined based on a literature review. The final values of six calibrated parameters were optimised for single sites as well as for multiple sites using generalised likelihood uncertainty estimation (GLUE) and model output conditioning that ensured plausible simulations based on user-defined ranges of carbon stock output variables (carbon stock in aboveground wood biomass, soil, and litter) and finding the intersections of site-specific plausible parameter hyperspaces. To support the model use, we tested the model performance by simulating aboveground tree wood, soil, and litter carbon across a large geographical gradient of central Europe and evaluated the trade-offs between parameters tailored to single plots and parameters estimated using multiple sites. Our findings indicated that parameter sets derived from single sites provided an improved local accuracy of simulations of aboveground wood, soil, and litter carbon stocks by 35 %, 55 %, and 11 % in comparison to the a priori parameter set. However, their broader applicability was very limited. A multi-site optimised parameter set, on the other hand, performed satisfactorily across the entire geographical domain studied here, including on sites not involved in the parameter estimation, but the errors were, on average, 26 %, 35 % and 9 % greater for the aboveground wood, soil, and litter carbon stocks than those obtained with the site-specific parameter sets. Importantly, model simulations demonstrated plausible responses across large-scale environmental gradients, featuring a clear production optimum of beech that aligns with empirical studies. These findings suggest that the model is capable of accurately simulating the dynamics of European beech across its range and can be used for more comprehensive experimentations.

UltraStat: Ultrafast Spectroscopy beyond the Fourier Limit Using Bayesian Inference.

The discrete Fourier transform (dFT) plays a central role in many ultrafast experiments, allowing the recovery of spectroscopic observables from time-domain measurements. In resonant experiments when population relaxation and coherence components of the signal coexist, the dFT is usually preceded by multiexponential fitting to remove the large population term. However, this procedure results in errors in both the recovered decay rates and the line shapes of the coherence spectral components. While other methods such as linear prediction singular value decomposition fit both terms simultaneously, they are limited to specific models that may not represent the true signal. These methods do not allow for systematic noise analysis or error estimation and require a priori knowledge of the signal rank. Here, we describe a general approach to parameter estimation in ultrafast spectroscopy─UltraStat─grounded in Bayesian analysis without the limitations set by Fourier theory. Using simulated, but realistic data, we demonstrate in a statistical sense how UltraStat provides accurate parameter estimation in the presence of many experimental constraints: noise, signal truncation, limited photon budget, and nonuniform sampling. UltraStat provides superior resolution compared to the dFT, up to an order of magnitude in cases where the line shapes are well-approximated. In these cases, we establish that primarily noise, not sampling, limits spectral resolution. Moreover, we show that subsampling may reduce the number of acquired points by 90% compared to the Nyquist-Shannon criteria. UltraStat greatly improves parameter estimation by providing statistically bound spectral and dynamics analysis, pushing the limits of ultrafast science.

Fixing imbalanced binary classification: An asymmetric Bayesian learning approach.

Most statistical and machine learning models used for binary data modeling and classification assume that the data are balanced. However, this assumption can lead to poor predictive performance and bias in parameter estimation when there is an imbalance in the data due to the threshold election for the binary classification. To address this challenge, several authors suggest using asymmetric link functions in binary regression, instead of the traditional symmetric functions such as logit or probit, aiming to highlight characteristics that would help the classification task. Therefore, this study aims to introduce new classification functions based on the Lomax distribution (and its variations; including power and reverse versions). The proposed Bayesian functions have proven asymmetry and were implemented in a Stan program into the R workflow. Additionally, these functions showed promising results in real-world data applications, outperforming classical link functions in terms of metrics. For instance, in the first example, comparing the reverse power double Lomax (RPDLomax) with the logit link showed that, regardless of the data imbalance, the RPDLomax model assigns effectively lower mean posterior predictive probabilities to failure and higher probabilities to success (21.4% and 63.7%, respectively), unlike Logistic regression, which does not clearly distinguish between the mean posterior predictive probabilities for these two classes (36.0% and 39.5% for failure and success, respectively). That is, the proposed asymmetric Lomax approach is a competitive model for differentiating binary data classification in imbalanced tasks against the Logistic approach.

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

ABSTRACT Pulsar timing arrays (PTA) can detect continuous nanohertz gravitational waves (GW) emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a GW from a single source. The modulation is the sum of terms proportional to the GW strain at the Earth and at every pulsar in the array. Here, we generalize previous state-space formulations of the PTA problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by 14 per cent. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

Moment Conditions for Dynamic Panel Logit Models with Fixed Effects

Abstract This paper investigates the construction of moment conditions in discrete choice panel data with individual specific fixed effects. We describe how to systematically explore the existence of moment conditions that do not depend on the fixed effects, and we demonstrate how to construct them when they exist. Our approach is closely related to the numerical “functional differencing” construction in Bonhomme (2012), but our emphasis is to find explicit analytic expressions for the moment functions. We first explain the construction and give examples of such moment conditions in various models. Then, we focus on the dynamic binary choice logit model and explore the implications of the moment conditions for identification and estimation of the model parameters that are common to all individuals.

Lack of identification of parameters in a simple behavioral macroeconomic model

Identifiability of the parameters is an important precondition for consistent estimation of models designed to describe empirical phenomena. Nevertheless, many estimation exercises proceed without a preliminary investigation into the identifiability of their models. As a consequence, the estimates could be essentially meaningless if convergence to the ‘true’ parameters is not guaranteed in the pertinent problem. We provide some evidence here that such a lack of identification is responsible for the inconclusive results reported in recent literature on parameter estimates for a certain class of nonlinear behavioral New Keynesian models. We also show that identifiability depends on the subtle details of the model structure. Hence, a careful investigation of identifiability should precede any attempt at estimation of such models.

Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein–Uhlenbeck Process with Application to U.S. Treasury Rate Analysis

Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein–Uhlenbeck process in probability, named the uncertain threshold Ornstein–Uhlenbeck process, filling the gaps of the corresponding research in uncertainty theory. We then explore the parameter estimation problem under different scenarios, including cases where certain parameters are known in advance while others remain unknown. Numerical examples are provided to illustrate our method proposed. We also apply the method to study the term structure of the U.S. Treasury rates over a specific period, which can be modeled by the uncertain threshold Ornstein–Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.

Evaluating Models of the Ageing BOLD Response.

Neural activity cannot be directly observed using fMRI; rather it must be inferred from the hemodynamic responses that neural activity causes. Solving this inverse problem is made possible through the use of forward models, which generate predicted hemodynamic responses given hypothesised underlying neural activity. Commonly-used hemodynamic models were developed to explain data from healthy young participants; however, studies of ageing and dementia are increasingly shifting the focus toward elderly populations. We evaluated the validity of a range of hemodynamic models across the healthy adult lifespan: from basis sets for the linear convolution models commonly used to analyse fMRI studies, to more advanced models including nonlinear fitting of a parameterised hemodynamic response function (HRF) and nonlinear fitting of a biophysical generative model (hemodynamic modelling, HDM). Using an exceptionally large sample of participants, and a sensorimotor task optimized for detecting the shape of the BOLD response to brief stimulation, we first characterised the effects of age on descriptive features of the response (e.g., peak amplitude and latency). We then compared these to features from more complex nonlinear models, fit to four regions of interest engaged by the task, namely left auditory cortex, bilateral visual cortex, left (contralateral) motor cortex and right (ipsilateral) motor cortex. Finally, we validated the extent to which parameter estimates from these models have predictive validity, in terms of how well they predict age in cross-validated multiple regression. We conclude that age-related differences in the BOLD response can be captured effectively by models with three free parameters. Furthermore, we show that biophysical models like the HDM have predictive validity comparable to more common models, while additionally providing insights into underlying mechanisms, which go beyond descriptive features like peak amplitude or latency, and include estimation of nonlinear effects. Here, the HDM revealed that most of the effects of age on the BOLD response could be explained by an increased rate of vasoactive signal decay and decreased transit rate of blood, rather than changes in neural activity per se. However, in the absence of other types of neural/hemodynamic data, unique interpretation of HDM parameters is difficult from fMRI data alone, and some brain regions in some tasks (e.g., ipsilateral motor cortex) can show responses that are more difficult to capture using current models.

Joint range and velocity super-resolution estimation with Doppler effects for innovative OFDM-based RFA RadCom system

Conventional radar and communication signals face challenges when integrating for accurate sensing in dense electromagnetic environments, especially in scenarios involving high-velocity targets estimation. To address this issue, we propose the random frequency agile-orthogonal frequency division multiplexing-based radar and communication (RFA-OFDM-based RadCom) signal, a novel framework that combines RFA hopping radar signal and OFDM signal. This framework effectively handles high-velocity Doppler scenarios, enhancing electronic countermeasure capabilities. In high-velocity scenarios, achieving accurate range and velocity estimation is crucial. We introduce a comprehensive received signal model that considers intrapulse and intersubcarrier Doppler effects, often overlooked in traditional high-velocity contexts. The proposed two-phase hierarchical perceptual methodology enables joint super-resolution estimation using the shared signal. We transform the shared signal echo model into a uniform linear array-like model and employ the matrix decomposition algorithm based on bidirectional weighted frequency smoothing (BWFS-MD) for decoherence processing. Subsequently, the estimation of signal parameters via rotational invariance techniques (ESPRIT)-complementary integrated subspace fitting (E-CISF) algorithm accurately estimates joint range and velocity. Meanwhile, the contrastive analysis of the mutual impacts between radar and communication functions is conducted. Theoretical analysis and simulation results robustly validate the superior performance of the proposed BWFS-MD algorithm. Furthermore, considering the precision of joint range-velocity estimation, real-time constraints, and super-resolution capability (which is emphasized), the E-CSIF algorithm demonstrates the best overall performance from a comprehensive perspective.

Confidence Interval Estimating the Mean of Normal Distribution and Skewed Distribution

The confidence interval is an important statistical estimator of population location and dispersion parameters. The purpose of this paper is to comprehend CI utilising various techniques. This includes classical CI, percentile bootstrap method, bootstrap-t and proposed bootstrap-t decile mean method. Distributions that are skewed and normal are used to generate data. The efficiency of the proposed method is evaluated on the basis of an extensive simulation study. The simulation findings show that the performance of the Student-t and three bootstrap approaches varies dramatically depending on sample size and skewness type. The coverage probability and length of the proposed confidence interval are compared with certain existing and widely used confidence intervals. For illustrative purposes, two real-life data sets are analysed, which, to some extent, support the simulation study conclusions. This paper's findings will be useful to a variety of researchers with practical experience in the fields of science and social sciences.

Adaptive fault estimation and accommodation for distributed parameter systems with coupled parabolic partial differential equations

This paper presents a novel model-based approach for fault detection, estimation and accommodation in linear distributed parameter systems (DPS) governed by parabolic partial differential equations (PDEs), prone to sensor and actuator faults. Unlike traditional methods, our approach utilises a filter-based observer directly employing the PDE representation and relies solely on boundary measurements, eliminating the need for extensive sensor arrays. By generating fault detection residuals from a comparison of measured and observer outputs, our method offers efficient fault detection. Innovative parameter update laws facilitate accurate estimation of fault parameters, enabling precise adjustment of the nominal controller to mitigate fault effects. Rigorous Lyapunov analysis ensures the robustness of our approach. Additionally, we derive a formula for estimating time-to-accommodation (TTA), providing valuable insights into fault resolution timelines. Simulations on a linearised diffusion process validate the effectiveness of our scheme, highlighting its superiority over existing approaches.

Reliability analysis based on doubly-truncated and interval-censored data

Field data provide important information on product reliability. Interval sampling is widely used for collection of field data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated (DT) data if the exact failure time is known. In many situations, the exact failure date is known only to fall within an interval, leading to doubly truncated and interval censored (DTIC) data. This article considers analysis of DTIC data under parametric failure time models. We consider a conditional likelihood approach and propose interval estimation for parameters and the cumulative distribution functions. Simulation studies show that the proposed method performs well for finite sample size.

Bearing remaining life prediction method based on ARAD -ELN and multi-stage wiener process

Abstract Stochastic process-based models are extensively utilized in health assessments and Remaining Useful Life (RUL) predictions of bearings. Nevertheless, bearings in actual operation undergo multiple degradation stages, each characterized by its unique trend of degradation. The application of a singular stochastic process for RUL prediction falls short of achieving optimal performance. Consequently, this paper introduces a multi-stage Wiener process-based approach for the prediction of bearings' RUL. Initially, to tackle the challenge of imbalanced sample sizes across different degradation stages of bearings, an ensemble learning-based neural network (ELN) enhanced by ARIMA Residual Anomaly Detection (ARAD) for the identification of bearing degradation stages is proposed. Subsequently, taking into account the temporal, unit-to-unit, and nonlinear variabilities of the degradation process at each stage, a Wiener process-based multi-stage degradation model for bearings is developed. A method for parameter estimation and updating, utilizing Kalman filtering and Maximum Likelihood Estimation (K-M) is introduced. Finally, the proposed model undergoes validation using both simulated data and the XJTU-SY bearing dataset. Experimental results of three RUL predictions show that the proposed method leads the benchmark model with RMSE values of 3.61, 2.92 and 7.24 respectively, affirming that the proposed model can precisely classify equipment degradation stages and predict RUL with high accuracy and stability.

Nonseparable panel models with index structure and correlated random effects

. To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution is established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation studies to assess finite-sample performance of the proposed estimator. We also use it to model dynamic earnings of women, and using our general identification results, we find a negative effect of the number of children not only on the selection into employment as usual, but also on the average earnings.

Precision comparison of intensity ratios and area ratios in spectral analysis

The long-debated question in analytical chemistry of which of the area ratio or the intensity ratio is the more precise has yielded no definitive analytical conclusion. To address this issue theoretically, we derived analytical solutions for the lower limits of estimation precision for spectral parameters, including the intensity ratio and area ratio, based on the Cramér–Rao lower bound (CRLB) framework for a Gaussian spectrum. The precisions of spectral parameter estimations from the analytical solutions were consistent with results obtained from Monte Carlo simulations. Our theoretical and simulation results revealed that the precision of estimating the area ratio surpassed that of the intensity ratio by a factor of 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{2}$$\\end{document}. Additionally, our experimental results aligned well with both theoretical predictions and simulation outcomes, further validating our approach. This increased precision of the area ratio is due to negative covariance between intensity and bandwidth, rather than the area containing more intensity information, as often misinterpreted. Consequently, and quite counter intuitively, prior bandwidth and intensity related information does not improve the area ratio precision: it worsens it. The analytical solution we derived represents the fundamental limits of spectral parameter measurement precision. Thus, it can be used as an alternative method for estimating the minimum error when experimental measurement uncertainty cannot be determined.

Comparative analysis of personal protective equipment nonadherence detection: computer vision versus human observers.

Human monitoring of personal protective equipment (PPE) adherence among healthcare providers has several limitations, including the need for additional personnel during staff shortages and decreased vigilance during prolonged tasks. To address these challenges, we developed an automated computer vision system for monitoring PPE adherence in healthcare settings. We assessed the system performance against human observers detecting nonadherence in a video surveillance experiment. The automated system was trained to detect 15 classes of eyewear, masks, gloves, and gowns using an object detector and tracker. To assess how the system performs compared to human observers in detecting nonadherence, we designed a video surveillance experiment under 2 conditions: variations in video durations (20, 40, and 60 seconds) and the number of individuals in the videos (3 versus 6). Twelve nurses participated as human observers. Performance was assessed based on the number of detections of nonadherence. Human observers detected fewer instances of nonadherence than the system (parameter estimate -0.3, 95% CI -0.4 to -0.2, P < .001). Human observers detected more nonadherence during longer video durations (parameter estimate 0.7, 95% CI 0.4-1.0, P < .001). The system achieved a sensitivity of 0.86, specificity of 1, and Matthew's correlation coefficient of 0.82 for detecting PPE nonadherence. An automated system simultaneously tracks multiple objects and individuals. The system performance is also independent of observation duration, an improvement over human monitoring. The automated system presents a potential solution for scalable monitoring of hospital-wide infection control practices and improving PPE usage in healthcare settings.

Nonhomogeneous hidden semi-Markov models for toroidal data

Abstract A nonhomogeneous hidden semi-Markov model is proposed to segment bivariate time series of wind and wave directions according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process’ survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates. It includes nonhomogeneous hidden Markov models and hidden semi-Markov models as special cases. Parameter estimates are obtained using an Expectation-Maximization algorithm that relies on an efficient augmentation of the latent process. Fitted on a time series of wind and wave directions recorded in the Adriatic Sea, the model offers a clear-cut description of sea state dynamics in terms of latent regimes and captures the influence of time-varying weather conditions on the duration of such regimes.

Cubic spline estimation for non parametric uncertain differential equation

. In the history of researching to estimate the unknown parameters that were in the uncertain differential equation (UDE), the problem of parameter estimation with known functional forms is often studied. However, in practical situations, its functional form is often unknown. In order to deal with this problem, this article proposes the cubic spline method to approximate the autonomous UDE, and perform non parametric estimation on it. The cross validation is introduced to determine the number of term (J), which is in the approximate cubic spline. In addition, the uncertain hypothesis testing is given to verify the rationality of this method. Finally, some numerical examples are given. Then this method is applied to a case study of the Beijing Air Quality Index, and a comparative analysis is given to verify the practicability and superiority of the cubic spline method.