Nonparametric Estimation Research Articles

Local linear estimator for fractional diffusions

In this paper, we investigate the nonparametric local linear estimator for the drift function of stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter [Formula: see text]. The drift function is one-sided dissipative Lipschitz that ensures the ergodic property of the SDE. We derive the strong consistency of the proposed estimator with proper bandwidth selectors associated with the determined Hurst parameter [Formula: see text]. The main tools are the ergodic theorem, Malliavin calculus, and a maximum inequality for It[Formula: see text]–Skorohod integrals.

Machine learning-based causal inference for evaluating intervention in travel behaviour research: A difference-in-differences framework

Causal inference with the difference-in-differences (DID) framework is popular in identifying causal effects with observational data and has started to be applied in recent travel behaviour studies. Most relevant transportation research adopts the conventional linear parametric DID model, which is known to be inflexible and restrictive. This study applies non-parametric DID estimators facilitated by machine learning (ML) models for causal inference in a variety of data scenarios. Semi-parametric and doubly robust estimators are established and integrated with the ML-based cross-fitting pipeline. Simulation studies and empirical case studies are conducted to showcase the ability of ML-based DID to detect causal effects from both simulated and real-world datasets. Results suggest that the proposed methods outperform conventional DID models in all data scenarios. Light working models are generally preferred over hyperparameter-dependent ones for their comparable performance, lower computational burden, and higher levels of compatibility to real-world empirical analysis. Empirical case studies also demonstrate how the proposed DID method could be applied to evaluate the impacts of various interventions on travel behaviour in different contexts. The present study adds to the existing travel behaviour literature by leveraging machine learning algorithms and non-parametric estimators to the impact evaluation of external interventions on travel characteristics and expanding the application of causal inference approaches in transportation research.

Further results involving residual and past extropy with their applications

In this paper we have investigated some stochastic aspects of residual extropy and past extropy. We then apply the results to the context of order statistics, coherent systems and record values. Nonparametric estimators for residual extropy and past extropy were introduced and their performance was illustrated using simulated data sets and real data sets.

Nonparametric estimation for periodic stochastic differential equations driven by [formula omitted]-Brownian motion

The paper is concerned with the nonparametric estimation problem for periodic stochastic differential equations driven by G-Brownian motion based on continuous observations. The consistency and asymptotic distribution of the nonparametric estimator are discussed. Computer simulations are performed to illustrate our theory.

Knowledge shortfalls and the effect of wildfires on biodiversity conservation in Guanajuato, Mexico

Knowledge of shortfalls could modify the geographic distribution patterns and limit the actions to conserve the biodiversity, even in the taxa best known. In addition, forest fires also could modify those patterns, but the potential effects of both factors have not been tested. Our aim was to analyze the effect of the Linnean and Wallacean shortfalls in the first evaluation of wildfire impacts on 22 amphibian and 13 mammal species distributed in Guanajuato, Mexico. We evaluated those shortfalls using the non-parametric estimator Chao2 and the Qs estimator and through maps of species richness patterns. To evaluate the effects of wildfires, we produced a fire recurrence map and quantified the burned area within species distributions and in 24 Protected Natural Areas (PNA) in the state. The Linnean shortfall showed some species missing to record in Guanajuato for both taxa, while the Wallacean shortfall showed poor quality of knowledge. Fire recurrence was high within 5 PNA. The richness patterns affected by fires covered nearly 17% of the surface of Guanajuato. Improving the knowledge of biogeographical patterns could provide better tools to stakeholders to decrease the negative impact of fires within PNA.

Nonparametric statistical inference for compound models

This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables ξ 1 + ⋯ + ξ N , where the number of summands, N, is a random variable independent of ξ 1 , ξ 2 , … Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of N, assuming that the distribution of ξ is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of N is not necessarily of Poisson type.

Approximations and inference for envelopment estimators of production frontiers

Nonparametric methods have been commonly used to assess the performance of both private and public organizations. Among them, the most popular ones are envelopment estimators such as Free Disposal Hull (FDH) or Data Envelopment Analysis (DEA), which estimate the attainable sets and their efficient boundaries by enveloping the cloud of observed units in the appropriate input-output space. However, these nonparametric envelopment techniques do not provide estimates of marginal products and other coefficients of economic interest. This paper presents a new approach that provides local estimates of all the desired partial derivatives and economic coefficients, which complement and complete the analysis based on nonparametric envelopment estimators. We improve nonparametric estimators by estimating nonparametrically smoothed efficient boundaries and providing derivatives and other coefficients without having to assume any parametric structure for the frontier and the inefficiency distribution. Our approach offers several advantages, such as a flexible nonparametric adjustment of the efficient frontier based on local linear models; a general multivariate efficiency model based on directional distances where one can choose the desired benchmark direction; the possibility of assessing the impact of external-environmental variables; a bootstrap-based statistical inference for deriving confidence intervals on the estimated coefficients for nonparametric and robust frontier approximations; the possibility of including factors aggregating inputs or outputs and recovering the estimated coefficients in the original units. To demonstrate the usefulness of the proposed approach, we provide an illustration in the field of education, where economic coefficients are important but the parametric assumptions have been questioned.

Age at natural menopause and its associated characteristics among Brazilian women: cross-sectional results from ELSI-Brazil.

This study aimed to determine the median age at natural menopause and analyze lifestyle, anthropometric, and dietary characteristics associated with the age at natural menopause among Brazilian women. This cross-sectional study involved 2,731 women 50 years and over, drawn from the baseline of the Brazilian Longitudinal Study of Aging (ELSI-Brazil, 2015/16). Nonparametric Kaplan-Meier cumulative survivorship estimates were used to assess the median timing of natural menopause. Cox proportional hazards regression models were employed to estimate the associations between age at natural menopause and exposure variables. The overall median age at natural menopause was 50 years. In the adjusted Cox model, current smoking (hazard ratio [HR], 1.11; 95% CI, 1.01-1.23) and underweight (HR, 1.34; 95% CI, 1.12-1.61) were associated with earlier natural menopause. Conversely, performing recommended levels of physical activity in the last week (HR, 0.88; 95% CI, 0.80-0.97), being overweight (HR 0.86; 95% CI, 0.74-0.99), and adhering to two or three healthy eating markers (HR, 0.80; 95% CI, 0.66-0.97; HR, 0.76; 95% CI, 0.61-0.94, respectively) were associated with later age at natural menopause. Binge drinking and waist circumference were not associated with age at natural menopause. Lifestyle, anthropometric, and dietary characteristics are significant factors that affect the age at natural menopause. Our findings can contribute to public policies targeted at Brazilian women's health.

Measurement-based Dynamic Modelling in Levitated Active Magnetic Bearing Systems

Commissioning Active Magnetic Bearings (AMB) requires a well-designed control system to reject external disturbances while supporting process loads. An accurate dynamic model is essential for predicting responses to various excitations and disturbances, aiding in controller design. Current models for AMB commissioning are either nonparametric estimations, which provide limited information, or finite element models, which may not capture all system dynamics. This paper presents a black-box method to develop a parametric model that captures all dynamics within an AMB system using measurement data. Frequency domain measurement data was used to construct a segmental linear model to simulate dynamic interactions. The controller, actuation, and sensor components were derived from SKF Magnetic Mechatronics design calculations to isolate the rotor from the plant model and reconstruct the closed-loop system model. The frequency response of the identified rotor model was compared to direct measurements, and the resulting system model was compared to direct measurements of the closed-loop response. Results show that the proposed segmental AMB system model predicts frequency response with 97.9% accuracy compared to direct measurements. This model will be used to design control methods to improve AMB system performance.

Nonparametric receiver operating characteristic curve analysis with an imperfect gold standard.

This article addresses the challenge of estimating receiver operating characteristic (ROC) curves and the areas under these curves (AUC) in the context of an imperfect gold standard, a common issue in diagnostic accuracy studies. We delve into the nonparametric identification and estimation of ROC curves and AUCs when the reference standard for disease status is prone to error. Our approach hinges on the known or estimable accuracy of this imperfect reference standard and the conditional independent assumption, under which we demonstrate the identifiability of ROC curves and propose a nonparametric estimation method. In cases where the accuracy of the imperfect reference standard remains unknown, we establish that while ROC curves are unidentifiable, the sign of the difference between two AUCs is identifiable. This insight leads us to develop a hypothesis-testing method for assessing the relative superiority of AUCs. Compared to the existing methods, the proposed methods are nonparametric so that they do not rely on the parametric model assumptions. In addition, they are applicable to both the ROC/AUC analysis of continuous biomarkers and the AUC analysis of ordinal biomarkers. Our theoretical results and simulation studies validate the proposed methods, which we further illustrate through application in two real-world diagnostic studies.

Accounting for imperfect detection when estimating species-area relationships and beta-diversity.

Ecologists have historically quantified fundamental biodiversity patterns, including species-area relationships (SARs) and beta diversity, using observed species counts. However, imperfect detection may often bias derived community metrics and subsequent community models. Although several statistical methods claim to correct for imperfect detection, their performance in species-area and β-diversity research remains unproven. We examine inaccuracies in the estimation of SARs and β-diversity parameters that emerge from imperfect detection, and whether such errors can be mitigated using a non-parametric diversity estimator (iNEXT.3D) and Multi-Species Occupancy Models (MSOMs). We simulated 28,350 sampling regimes of 2835 fragmented communities, varying the mean and standard deviation of species detection probabilities, and the number of sampling repetitions. We then quantified the bias, accuracy, and precision of derived estimates of model coefficients for SARs and the effects of patch area on β-diversity (pairwise Sørensen similarity). Imperfect detection biased estimates of all evaluated parameters, particularly when mean detection probabilities were low, and there were few sampling repetitions. Observed counts consistently underestimated species richness and SAR z-values, and overestimated SAR c-values; iNEXT.3D and MSOMs only partially resolved these biases. iNEXT.3D provided the best estimates of SAR z-values, although MSOM estimates were generally comparable. All three methods accurately estimated pairwise Sørensen similarity in most circumstances, but only MSOMs provided unbiased estimates of the coefficients of models examining covariate effects on β-diversity. Even when using iNEXT.3D or MSOMs, imperfect detection consistently caused biases in SAR coefficient estimates, calling into question the robustness of previous SAR studies. Furthermore, the inability of observed counts and iNEXT.3D to estimate β-diversity model coefficients resulted from a systematic, area-related bias in Sørensen similarity estimates. Importantly, MSOMs corrected for these biases in β-diversity assessments, even in suboptimal scenarios. Nonetheless, as estimator performance consistently improved with increasing sampling repetitions, the importance of appropriate sampling effort cannot be understated.

Study of Experimental and Assembly Uncertainties on Modal Parameter Estimates of Axial Piston Pumps

Finite Element Model Updating (FEMU) plays a pivotal role in enhancing the accuracy and reliability of structural dynamics models. Nonetheless, uncertainties related to experimental vibration testing and natural manufacturing variability introduce unavoidable variability in the results of Modal Parameter Extraction (MPE), which is the basis for updating. In this regard, this study delves into the inherent variability of estimates from MPE following from experimental vibration testing Axial Piston Pumps (APPs). Accordingly, we investigate the effect of material properties, boundary conditions and measurement noise, through several experimental vibration tests involving assembly-disassembly and exchange of components. These variations account for inherent manufacturing variability and tolerances both at the component and material level. The obtained vibration data is processed using non-parametric FRF estimates and the Stochastic Subspace Identification (SSI) algorithm, resulting in a collection of FRFs and modal parameter estimates (natural frequencies, damping ratios and mode shapes). We use multivariate analysis techniques to quantify the uncertainty of these estimates and to assess the individual effect of assembly and population uncertainties. These results serve as a basis for further investigation towards the updating of a FE model of the APP, and the quantification of modal parameter uncertainties within the material and substructure connectivity properties.

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

Medical Data for the Nadaraya-Watson Kernel Method in Nonparametric Regression Models Based on Hyperbolic Secant Function

Nonparametric kernel estimates used in this work aim to compare different treatment options by examining the recorded medical data. The following use of the suggested strategy depends on a kernel function and a parameter called bandwidth. The Nadaraya-Watson kernel (NWK) estimation is a necessary nonparametric kernel estimator used in regression models. A new Nadaraya-Watson regression estimate depends on the hyperbolic secant kernel (HSK) with fixed bandwidth (FNW) and Variable Bandwidth (VNW) is proposed.. We calculated some properties of the unknown regression function estimator, including bias, variance, optimal bandwidth, and a global measure of error criterion mean square error. Finally, simulation and three real data sets are used to evaluate its performance. Results from simulation and real data showed that the VNW using HSK is more effective than the FNW based on Average Mean Square Error Criterion. Also, Nadaraya-Watson using HSK function is more effective than Nadaraya-Watson using the Gaussian kernel density function.

A comprehensive phenotypic and genotypic evaluation of Spanish groundnuts from diverse crosses to identify superior and stable donors for fresh seed dormancy

Breeding high yielding groundnut cultivars with 2–3 weeks of fresh seed dormancy, particularly in Spanish-type cultivars, enhances the sustainability of agriculture in groundnuts. In this context, we conducted a comprehensive phenotypic and genotypic evaluation of advanced breeding lines developed in the genetic background of Spanish types. By employing multi-phenotyping and marker data, we identified PBS 15044, 16004, 16013, 16015, 16016, 16017, 16020, 16021, 16026, 16031, 16035, 16037, 16038, 16039, 16041, and 16042 with 2–3 weeks dormancy (> 90%).The various parametric and non-parametric estimates identified the stable fresh dormant genotypes with one or more superior economic trait. PBS 16021, 15044, 16038, and 16039 identified with high hundred pod weight (HPW) were also reported having high intensity of dormancy (> 90% for up to 3 weeks); PBS 15044, 16016, PBS 16038 and PBS 16039 with high hundred kernel weight (HKW) also reported with up to 3 weeks fresh seed dormancy; and PBS 16013, 16031, and 16038 with up to 3 weeks fresh seed dormancy had high shelling percentage (SP). They can be used to develop lines with the desired level of dormancy, and high yields, by designing appropriate breeding strategies.

Non-parametric identification and testing of quantal response equilibrium

This paper studies the falsifiability and identification of Quantal Response Equilibrium (QRE) when each player's utility and error distribution are relaxed to be unknown non-parametric functions. Using the variation of players' choices across a series of games, we first show that both the utility function and the distribution of errors are non-parametrically over-identified. This over-identification result further suggests a straightforward testing procedure for QRE which achieves the desired type-1 error and maintains a small type-2 error. To apply this methodology, we conduct an experimental study of the matching pennies game. Our non-parametric estimates strongly reject the conventional Logit choice probability. Moreover, when the utility and the error distribution are sufficiently flexible and heterogeneous, the quantal response hypothesis cannot be rejected for 70% of participants. However, strong assumptions such as linear utility, logistically distributed errors, and homogeneity lead to substantially higher rejection rates.

Estimation of counterfactual distributions with a continuous endogenous treatment

In this article, I propose a method to estimate the counterfactual distribution of an outcome variable when the treatment is endogenous, continuous, and its effect is heterogeneous. The types of counterfactuals considered are those in which the change in treatment intensity can be correlated with the individual effects or when some of the structural functions are changed by some other group’s counterparts. I characterize the outcome and the treatment with a triangular system of equations in which the unobservables are related by a copula that captures the endogeneity of the treatment, which is nonparametrically identified by inverting the quantile processes that determine the outcome and the treatment. Both processes are estimated using existing quantile regression methods, and I propose a parametric and a nonparametric estimator of the copula. To illustrate these methods, I estimate several counterfactual distributions of the birth weight of children, had their mothers smoked differently during pregnancy.

Counterfactual copula

This paper proposes a nonparametric estimator of the counterfactual copula of two outcome variables that would be affected by a policy intervention. The proposed estimator allows policymakers to conduct ex ante evaluations by comparing the estimated counterfactual and actual copulas as well as their corresponding association measures. Asymptotic properties of the counterfactual copula estimator are established under regularity conditions. These conditions are also used to validate the nonparametric bootstrap for inference on counterfactual quantities. Simulation results indicate that our estimation and inference procedures perform well in moderately sized samples.

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The importance of understanding auxiliary insects in agroecosystems has become increasingly necessary due to the overuse of chemical products that disturb their presence and sometimes lead to their extermination without our awareness of their existence. The objective of this research project is to conduct the first inventory of aphid parasitoids in the Aphidiinae subfamily in orange orchards in the Guelma Region (Eastern Algeria) and to estimate the number of species present in this region using four non-parametric estimators. The results revealed the presence of ten species, namely Aphidius matricariae (Haliday, 1834), Aphidius sp., A. ervi (Haliday, 1834), Binodoxys angelicae (Haliday, 1833), B. acalephae (Marshall, 1896), Diaeretiella rapae (McIntosh, 1855), Ephedrus plagiator (Nees, 1811), Praon volucre (Haliday, 1833), Lipolexis gracilis (Foerster, 1862), and Lysiphlebus testaceipes (Cresson, 1880) .Among these species, L. testaceipes, B. angelicae, and A. matricariae were the most dominant during the study period. Binodoxys acalephae, despite being present in small numbers, had a ubiquitous ecological status, while A. matricariae, A. ervi, B. angelicae, D. rapae, and L. testaceipes maintained a constant status. According to the non-parametric estimators, the number of species varied, but the average was 11.39 ± 0.54 species, indicating that the richness could increase to 12 with a sampling accuracy of 87.74%. Despite their low abundance, the richness of Aphidiinae species in the orange orchards could be used in a biological control context.

Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects.

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically-for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal-with a view to inform nonparametric inference.