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This article proposes a new method for examining the impact on a firm's investment of uncertainty reflected in its stock-return volatility. We simultaneously address the endogeneity of uncertainty and mismeasurement in Tobin's Q , but earlier empirical work often neglects one of the two issues. Our nonparametric estimates further suggest that the relation between investment and uncertainty is significantly decreasing and strongly concave. This result contrasts with the existing literature that widely adopts linear regressions. Ignoring nonlinearity or measurement error in Q can lead to a substantial estimation bias. However, the bias due to the endogeneity of uncertainty is small. [ABSTRACT FROM AUTHOR]

This article pays attention to the generalized edge frequency polygon. By taking weighted averages of the heights in the neighbouring $ 2k (k\geq 1) $ 2 k (k ≥ 1) bins, we can reduce the asymptotic mean integrated squared error than that of the frequency polygon estimator. As a density estimator based on histogram technique, the generalized edge frequency polygon has the advantage of computational simplicity and has been widely used in many fields. The purpose of this article is to investigate the weak consistency, the uniformly weak consistency and the rate of the uniformly weak consistency for generalized edge frequency polygon of density function under α-mixing samples, which improve and extend those of frequency polygon in the literature. In particular, the simulation study and real data analysis based on finite samples are performed to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite-length time series, while the variance of the estimator decreases as the number of segments increases, the magnitude of the estimator's bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing a novel method for debiasing Welch's method that maintains the computational complexity and asymptotic consistency, and leads to improved finite-sample performance. Theoretical results are given for fourth-order stationary processes with finite fourth-order moments and an absolutely convergent fourth-order cumulant function. The significant bias reduction is demonstrated with numerical simulation and an application to real-world data. Our estimator also permits irregular spacing over frequency and we demonstrate how this may be employed for signal compression and further variance reduction. The code accompanying this work is available in R and python. [ABSTRACT FROM AUTHOR]

This paper develops a nonparametric method for estimating the spectral density of multivariate stationary time series using basis expansion. A likelihood-based approach is used to fit the model through the minimization of a penalized Whittle negative log-likelihood. Then, a Newton-type algorithm is developed for the computation. In this method, we smooth the Cholesky factors of the multivariate spectral density matrix in a way that the reconstructed estimate based on the smoothed Cholesky components is consistent and positive-definite. In a simulation study, we have illustrated and compared our proposed method with other competitive approaches. Finally, we apply our approach to two real-world problems, Electroencephalogram signals analysis, E l N i n ~ o Cycle. [ABSTRACT FROM AUTHOR]

We investigate the nonparametric additive regression estimation in random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function and its univariate additive components belong to Besov space. We consider the problem under two noise structures; (1) homoskedastic Gaussian long memory errors and (2) heteroskedastic Gaussian long memory errors. In the homoskedastic long-memory error case, the estimator is completely adaptive with respect to the long-memory parameter. In the heteroskedastic long-memory case, the estimator may not be adaptive with respect to the long-memory parameter unless the heteroskedasticity is of polynomial form. In either case, the convergence rates depend on the long-memory parameter only when long-memory is strong enough, otherwise, the rates are identical to those under i.i.d. errors. In addition, convergence rates are free from the curse of dimensionality. [ABSTRACT FROM AUTHOR]

We investigate the asymptotic properties of a kernel-type nonparametric estimator of the linear multiplier in models governed by a stochastic differential equation driven by a general Gaussian process. [ABSTRACT FROM AUTHOR]

The volume under the receiver operating characteristic (ROC) surface (VUS) is a natural generalization of a classical tool, the area under the ROC curve from a disease with two statuses (e.g., healthy and diseased) to a disease with a three-class status (e.g., healthy, intermediate, and diseased) for evaluating the effectiveness of a continuous biomarker in discriminating the disease status. In this work, we discuss the problem of estimating VUS using ranked set sampling (RSS), a cost-efficient alternative to simple random sampling (SRS), which is applicable in situations in which the actual quantification of the biomarker is hard, time-consuming, costly or tedious but a small number of sample units can still be ordered without referring to their precise values. We develop several nonparametric estimators when SRS or RSS design is applied to each of the healthy, intermediate and diseased subpopulations. We study the properties of the proposed estimators, including unbiasedness, variance expression, asymptotic normality, and efficiency. Specifically, we show that the introduced estimators are at least as efficient as their SRS counterparts and often far more efficient under a large class of imperfect ranking models. Lastly, to demonstrate the applicability and efficiency of the introduced procedures in an environmental context, we apply them to a real environmental dataset, utilizing three of its five classes. [ABSTRACT FROM AUTHOR]

Adaption to prices is an important feature of productivity development. This paper proposes an extension of the StoNED model to accommodate estimation of allocative efficiency. It demonstrates how indirect production theory is suited for assessing allocative efficiency and helps alleviating the curse of dimensionality for stochastic nonparametric estimators compared to conventional measures of allocative efficiency. Furthermore, the paper elaborates on the appropriate cost of capital for the estimation of allocative efficiency. The proposed model framework is utilized to study allocative efficiency of Norwegian container ports, thereby adding to the literature on seaport terminal efficiency studies. [ABSTRACT FROM AUTHOR]

The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula. [ABSTRACT FROM AUTHOR]

AbstractIn the context of reliability and survival analysis, the observed lifetimes are often subject to left, right, or double truncation. Doubly truncated data usually arises when information about the lifetime of a system is available only within a particular time interval. In this paper, we consider the stress-strength reliability measure for the doubly truncated data. Several properties of this measure, including bounds and the effect of monotonic transformations, are discussed. Further, we propose a nonparametric estimator for doubly truncated stress-strength reliability, and its asymptotic properties are studied. A simulation study is also carried out to evaluate the performance of the asymptotic confidence interval and the percentile bootstrap interval for doubly truncated stress-strength reliability. Finally, the proposed estimation procedure is applied to a real data set for illustration. [ABSTRACT FROM AUTHOR]

AbstractThe randomized response technique offers an effective way for reducing potential bias resulting from nonresponse and untruthful responses when asking questions about sensitive behaviors or beliefs. The technique is also used for conducting statistical disclosure control of public use data files released by statistical agencies such as the U.S. Census Bureau. In both cases, the technique works by randomizing the actual survey responses using some known randomization model. In the case of asking sensitive survey questions, the randomization of responses is done by the survey respondents and only the randomized responses are collected, whereas in the case of disclosure control, the survey agency implements the randomization of responses after collecting the survey data and prior to releasing it for public use. This paper considers estimating the finite population mean from a survey where randomized responses are available for the study variable along with complete non-randomized auxiliary information. We define and study a class of nonparametric model-assisted estimators that make efficient use of the available auxiliary information and account for the complex survey design. The asymptotic properties of the proposed estimators are derived and a bootstrap variance estimator is presented. The finite sample performance of the proposed estimators is studied via extensive simulations accounting for a wide range of forms for the relationship between the study variable and auxiliary variable. The empirical results support the theoretical analyses and suggest that our proposed estimators are superior to existing estimators in most cases. Furthermore, the proposed methods are illustrated using real data from the 2015 U.S. consumer expenditure survey. [ABSTRACT FROM AUTHOR]

AbstractAn integer time series is a sequence of discrete integers arranged chronologically to represent a specific event or phenomenon. It may include negative integers, and its behavior can be influenced by variations in covariates. To address these complexities, this paper introduces a p-order signed integer-valued autoregressive model with time-varying coefficients. Considering the presence of zero-inflated phenomena, we specifically employ the zero-inflated Skellam distribution. To estimate the unknown parameters and nonparametric functions in our proposed model, we adopt a two-step iterative process that combines local linear estimation with either conditional least squares or conditional maximum likelihood. Through a comprehensive simulation study, we evaluate the performance of our estimation method and demonstrate the usefulness of the proposed model using a real-life dataset. [ABSTRACT FROM AUTHOR]

Several approaches to estimating the productivity function for a Hawkes point process with variable productivity are discussed, improved upon, and compared in terms of their root-mean-squared error and computational efficiency for various data sizes, and for binned as well as unbinned data. We find that for unbinned data, a regularized version of the analytic maximum likelihood estimator proposed by Schoenberg is the most accurate but is computationally burdensome. The unregularized version of the estimator is faster to compute but has lower accuracy, though both estimators outperform empirical or binned least squares estimators in terms of root-mean-squared error, especially when the mean productivity is 0.2 or greater. For binned data, binned least squares estimates are highly efficient both in terms of computation time and root-mean-squared error. An extension to estimating transmission time density is discussed, and an application to estimating the productivity of Covid-19 in the United States as a function of time from January 2020 to July 2022 is provided. [ABSTRACT FROM AUTHOR]

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias. [ABSTRACT FROM AUTHOR]

Chesneau et al. (Journal of Computational and Applied Mathematics, 2020) study nonparametric wavelet estimations over L 2 risk of a regression model with additive and multiplicative noises. This paper considers convergence rates over L p (1 ≤ p < + ∞) risk of linear wavelet estimator and nonlinear wavelet estimator under some mild conditions. It turns out that our results reduce to the theorems of Chesneau et al., when p = 2 . [ABSTRACT FROM AUTHOR]

In this article, we consider the wavelet estimation of copula density for negatively superadditive dependent random variables. Using wavelet methods, we propose and develop a new estimation procedure for this problem. In particular, a BlockShrink estimator is constructed and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The main result is prepared to display the performance of the wavelet-based estimator and a simulation study to compare the behavior of the proposed wavelet estimator with the kernel copula density estimator are also given. Finally, we consider a real life application in hydrology for rainfall intensity data. [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the local linear k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors of the constructed estimators. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The usefulness of our result for the smoothing parameter automatic selection is discussed. Some simulation studies are carried out to show the finite sample performances of the kNN estimator. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in functional data analysis. [ABSTRACT FROM AUTHOR]

Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability θ : = P (X < Y) based on independent random samples from the distributions of X ′ , Y ′ , ζ and η , where X ′ = X + ζ , Y ′ = Y + η and X, Y, ζ , η are mutually independent random variables. In this context, ζ , η are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for θ depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of ζ , η only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, ζ and η , we obtain some upper and lower bounds on the convergence rate of the estimator. A numerical example is also given to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

Firstly, in this study, we utilize the high-order element model (truss link model) simulation method in OpenSees (3.7.0) software and verify the feasibility of this method by comparing it with the shaking table test. Secondly, the structural dynamic response of adjacent structures with different performance levels, spacing, and layout forms under large earthquakes is analyzed, and the corresponding structural failure probability is studied. Furthermore, the life distribution within the design service life of the structure is predicted according to the nonparametric Kaplan–Meier estimation model. Finally, the reliability of adjacent structures is evaluated by using the joint engineering demand parameters. The analysis method of replacing the theoretical analysis based on engineering experience and certainty in the current specification with probability analysis is proposed, which provides a more reliable theoretical basis for decision-making regarding the reinforcement, maintenance, or demolition of structures in the later stage. [ABSTRACT FROM AUTHOR]

Abstract.The random coefficients model Yi=β0i+β1iX1i+β2iX2i+…+βdiXdi, with 퐗i, Yi, 휷i i.i.d, and 휷i independent of 퐗i is often used to capture unobserved heterogeneity in a population. We propose a quasi-maximum likelihood method to estimate the joint density distribution of the random coefficient model. This method implicitly involves the inversion of the Radon transformation in order to reconstruct the joint distribution, and hence is an inverse problem. To add stability to the solution, we apply Tikhonov-type regularization methods. Nonparametric estimation for the joint density of βi=(β0i,…,βdi) based on kernel methods or Fourier inversion have been proposed in recent years. Most of these methods assume a heavy tailed design density f퐗. We analyze the convergence of the quasi maximum likelihood method without assuming heavy tails for f퐗 and illustrate performance by applying the method on simulated and real data. [ABSTRACT FROM AUTHOR]

Recent literature has found conditional transition rates to be a useful tool for avoiding Markov assumptions in multi-state models. While the estimation of univariate conditional transition rates has been extensively studied, the intertemporal dependencies captured in the bivariate conditional transition rates still require a consistent estimator. We provide an estimator that is suitable for censored data and emphasiz e the connection to the rich theory of the estimation of bivariate survival functions. Bivariate conditional transition rates are necessary for various applications in the survival context but especially in the calculation of moments in life insurance mathematics. [ABSTRACT FROM AUTHOR]

AbstractLet θ=P(XY are independent random variables, with known constants μX,μZ∈R, σ>0. Suppose we observe a random sample Y1′,…,Yn′ from the distribution of Y′=Y+ε. Here ε is a random error and distributed with a known continuous distribution. Our aim is to estimate θ based on the sample as well as on the complete knowledge about the distributions of X, Z and ε. We propose a nonparametric estimator of θ by applying the Fourier deconvolution method. Our estimator is shown to be mean consistent with respect to the mean squared error and strongly consistent. Under some regularity assumptions on the densities of Y and ε, some error estimates of the proposed estimator are derived. A simulation study is also conducted to illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In survival analysis, it is possible to have some data which are both positively dependent and corrupted by additive noise. This occurs due to the presence of measurement errors. The main focus of this paper is the nonparametric estimation of the hazard rate function in terms of the deconvolution kernel density estimator f n (x) and the distribution function estimator obtained by integrating f n (x). We aim at establishing a strong uniform consistency with rates. The performance quality of the hazard function estimator is evaluated numerically. Finally, the approach is implemented to estimate the length of pregnancy from a real data set. [ABSTRACT FROM AUTHOR]

The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good. [ABSTRACT FROM AUTHOR]

Consider a diffusion process X = (X t) t ∈ [ 0 , 1 ] observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus on the nonparametric estimation of the diffusion coefficient. We propose ridge estimators of the square of the diffusion coefficient from discrete observations of X that are obtained by minimization of the least squares contrast. We prove that the estimators are consistent and derive rates of convergence as the number of observations tends to infinity. Two observation schemes are considered in this paper. The first scheme consists in one diffusion path observed at discrete times, where the discretization step of the time interval [0, 1] tends to zero. The second scheme consists in repeated observations of the diffusion process X, where the number of the observed paths tends to infinity. The theoretical results are completed with a numerical study over synthetic data. [ABSTRACT FROM AUTHOR]

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm. [ABSTRACT FROM AUTHOR]

Information-theoretic measures play a vital role in training learning systems. Many researchers proposed non-parametric entropy estimators that have applications in adaptive systems. In this work, a kernel density estimator using Kapur entropy of order a and type ß has been proposed and discussed with the help of theorems and properties. From the results, it has been observed that the proposed density measure is consistent, minimum, and smooth for the probability density function (PDF) underlying given conditions and validated with the help of theorems and properties. The objective of the paper is to understand the theoretical viewpoint behind the underlying concept. [ABSTRACT FROM AUTHOR]

This paper investigates the finite sample performance of a range of parametric, semi-parametric, and non-parametric instrumental variable estimators when controlling for a fixed set of covariates to evaluate the local average treatment effect. Our simulation designs are based on empirical labor market data from the US and vary in several dimensions, including effect heterogeneity, instrument selectivity, instrument strength, outcome distribution, and sample size. Among the estimators and simulations considered, non-parametric estimation based on the random forest (a machine learner controlling for covariates in a data-driven way) performs competitive in terms of the average coverage rates of the (bootstrap-based) 95% confidence intervals, while also being relatively precise. Non-parametric kernel regression as well as certain versions of semi-parametric radius matching on the propensity score, pair matching on the covariates, and inverse probability weighting also have a decent coverage, but are less precise than the random forest-based method. In terms of the average root mean squared error of LATE estimation, kernel regression performs best, closely followed by the random forest method, which has the lowest average absolute bias. [ABSTRACT FROM AUTHOR]

AbstractAdvancements in technology have elevated the prominence of 3D point cloud data, making its analysis increasingly vital across various applications. This need drives the demand for advanced statistical analytic approaches to handle challenges such as size, sparsity, and irregularity in 3D point clouds while ensuring accurate and efficient information extraction. This article introduces a novel nonparametric distributed (NPD) learning framework that uses trivariate spline smoothing over a triangulation of domain. The proposed NPD algorithm features a straightforward, scalable, and communication-efficient implementation scheme that can achieve near-linear speedup. In addition, we provide rigorous theoretical support for the NPD estimation framework and demonstrate that the NPD spline estimators attain the same convergence rate as the global spline estimators obtained using the entire dataset and achieve the optimal nonparametric convergence rate established by Stone under some regularity conditions. To evaluate the efficacy of the proposed NPD method, we conduct simulation studies comparing it with several global nonparametric estimation methods used to smooth the 3D data. The results demonstrate the superior performance of the NPD method in accurately and efficiently processing and learning from 3D point clouds, highlighting its potential to advance large and complex data analysis. Supplementary material, which contains related technical details, proofs of the theoretical results, and additional results in simulation studies, is available online. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonparametric estimator of ruin probability in the Wiener–Poisson risk model based on high-frequency data. The estimator is constructed via the Fourier-cosine method and the threshold technique, and the convergence rate is also studied for a large sample size. Finally, we verify the effectiveness of our estimator through some simulation studies. [ABSTRACT FROM AUTHOR]

This study employs rolling quantile regression and non-parametric estimation methods, specifically Quantile-on-Quantile (QQ) and Causality-in-Quantiles (QC), to investigate the impact of uncertainty indices (Geopolitical Uncertainty (GPR), Climate Policy Uncertainty (CPU), and Economic Policy Uncertainty (EPU)) on China's agricultural commodity futures. The rolling window quantile regression coefficients vary over time, with CPU having the most significant impact on agricultural commodity futures. The empirical results from the non-parametric estimation QQ method reveal when agricultural commodities are in a prosperous market, CPU and EPU exhibit relatively strong correlation, while GPR shows weaker or insignificant correlation. According to the non-parametric estimation QC method, the evidence suggests that the second-order (variance) causality relationship is relatively stronger than the first-order (mean) causality relationship, and the first-order mean causal relationship between CPU and corn and between EPU and wheat is not significant across the entire range of quantiles. The results on Hedging Effectiveness reveal that the efficiency of uncertainty hedging is substantiated. The hedging effectiveness of EPU exhibits improvement post-COVID-19, whereas the effectiveness of GPR and CPU is more pronounced in the pre-COVID-19 period. [ABSTRACT FROM AUTHOR]

Many existing methodologies for analyzing spatiotemporal point patterns are developed based on the assumption of stationarity in both space and time for the second-order intensity or pair correlation. In practice, however, such an assumption often lacks validity or proves to be unrealistic. In this paper, we propose a novel and flexible nonparametric approach for estimating the second-order characteristics of spatiotemporal point processes, accommodating non-stationary temporal correlations. Our proposed method employs kernel smoothing and effectively accounts for spatial and temporal correlations differently. Under a spatially increasing-domain asymptotic framework, we establish consistency of the proposed estimators, which can be constructed using different first-order intensity estimators to enhance practicality. Simulation results reveal that our method, in comparison with existing approaches, significantly improves statistical efficiency. An application to a COVID-19 dataset further illustrates the flexibility and interpretability of our procedure. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Bahadur type representation of a nonparametric expected shortfall estimator for α -mixing financial losses. Based on the Bahadur type representation, we further establish the Berry–Esseen bound of the nonparametric expected shortfall estimator. It is shown that the optimal rate can achieve nearly O (n - 1 / 8) under some appropriate conditions. We also carry out some numerical simulations and a real data example to support our theoretical results based on finite samples. [ABSTRACT FROM AUTHOR]

In system reliability, practitioners may be interested in testing the homogeneity of the component lifetime distributions based on system lifetimes from multiple data sources for various reasons, such as identifying the component supplier that provides the most reliable components. In this paper, we develop distribution-free hypothesis testing procedures for the homogeneity of the component lifetime distributions based on system lifetime data when the system structures are known. Several nonparametric testing statistics based on the empirical likelihood method are proposed for testing the homogeneity of two or more component lifetime distributions. The computational approaches to obtain the critical values of the proposed test procedures are provided. The performances of the proposed empirical likelihood ratio test procedures are evaluated and compared to the nonparametric Mann–Whitney U test and some parametric test procedures. The simulation results show that the proposed test procedures provide comparable power performance under different sample sizes and underlying component lifetime distributions, and they are powerful in detecting changes in the shape of the distributions. [ABSTRACT FROM AUTHOR]

This paper presents several nonparametric estimators for the Sharma–Taneja–Mittal entropy measure of a continuous random variable with known support, utilizing spacing, a local linear model, and a kernel function. The properties of these estimators are discussed. Their performance was also examined through real data analysis and Monte Carlo simulations. In the Monte Carlo experiments, the proposed Sharma–Taneja–Mittal entropy estimators were employed to create a test of goodness-of-fit under the standard uniform distribution. The suggested test statistics demonstrate strong performance, as evidenced by a comparison of their power with that of other tests for uniformity. Finally, we examine a classification issue in the recognition of patterns to underscore the significance of these measures. [ABSTRACT FROM AUTHOR]

A new efficient nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to estimation of inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the discrete cosine transform is proposed. [ABSTRACT FROM AUTHOR]

We propose a new threshold selection method for nonparametric estimation of the extremal index of stochastic processes. The discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability density function. Now it is modified to select a threshold parameter of an extremal index estimator. A modification of the discrepancy statistic based on the Cramér–von Mises–Smirnov statistic $ \omega ^2 $ ω 2 is calculated by k largest order statistics instead of an entire sample. Its asymptotic distribution as $ k\to \infty $ k → ∞ is proved to coincide with the $ \omega ^2 $ ω 2 -distribution. Its quantiles are used as discrepancy values. The convergence rate of an extremal index estimate coupled with the discrepancy method is derived. The discrepancy method is used as an automatic threshold selection for the intervals and K-gaps estimators. It may be applied to other estimators of the extremal index. The performance of our method is evaluated by simulated and real data examples. [ABSTRACT FROM AUTHOR]

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. 'Semiparametric Zero-Inflated Bernoulli Regression with Applications', Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study. [ABSTRACT FROM AUTHOR]

The paper introduces a nonparametric estimator for the regression function of left truncated and right censored data, achieved through minimising the mean squared relative error. Under α-mixing condition, strong uniform convergence of the estimator is established with a rate over a compact set. An extensive simulation study is conducted to assess the estimator's performance, comparing its efficiency to that of the classical regression estimator for finite samples across various scenarios. Moreover, a real world application is presented to demonstrate the practical utility of the proposed estimator. [ABSTRACT FROM AUTHOR]

We discuss nonparametric estimation of the trend coefficient in models governed by a stochastic differential equation driven by a Gaussian process with small noise. [ABSTRACT FROM AUTHOR]

Interacting particle or agent systems that exhibit diverse swarming behaviors are prevalent in science and engineering. Developing effective differential equation models to understand the connection between individual interaction rules and swarming is a fundamental and challenging goal. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of N particles in \mathbb {R}^d under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of the interaction function with pointwise uncertainty quantification, and the other is the inference of unknown scalar parameters in the noncollective friction forces of the system. We formulate the learning problem as a statistical inverse learning problem and introduce an operator-theoretic framework that provides a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. Given data collected from M i.i.d trajectories with independent Gaussian observational noise, we provide a finite-sample analysis, showing that our posterior mean estimator converges in a Reproducing Kernel Hilbert Space norm, at an optimal rate in M equal to the one in the classical 1-dimensional Kernel Ridge regression. As a byproduct, we show we can obtain a parametric learning rate in M for the posterior marginal variance using L^{\infty } norm and that the rate could also involve N and L (the number of observation time instances for each trajectory) depending on the condition number of the inverse problem. We provide numerical results on systems exhibiting different swarming behaviors, highlighting the effectiveness of our approach in the scarce, noisy trajectory data regime. [ABSTRACT FROM AUTHOR]

Hyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods. [ABSTRACT FROM AUTHOR]

We study the multiclass classification problem where the features come from a mixture of time‐homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug‐in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of convergence under different set of assumptions. Finally, a numerical study supports our theoretical findings. [ABSTRACT FROM AUTHOR]

This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure. [ABSTRACT FROM AUTHOR]

This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence. [ABSTRACT FROM AUTHOR]

We provide a framework for motivating and diagnosing the functional form in the structural part of nonlinear or linear structural equation models when the measurement model is a correctly specified linear confirmatory factor model. A mathematical population-based analysis provides asymptotic identification results for conditional expectations of a coordinate of an endogenous latent variable given exogenous and possibly other endogenous latent variables, and theoretically well-founded estimates of this conditional expectation are suggested. Simulation studies show that these estimators behave well compared to presently available alternatives. Practically, we recommend the estimator using Bartlett factor scores as input to classical non-parametric regression methods. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics used to model quantities derived from responses of multiple subjects. These statistics extend the concept of the empirical mean of a d-variate random variable X by considering sums over all distinct m-tuples of observations of X. Within this realm, W. Stute [134] introduced conditional U-statistics, a generalization of the Nadaraya-Watson estimators for regression functions, and demonstrated their strong point-wise consistency. This paper presented a first theoretical examination of the Dirichlet kernel estimator for conditional U-statistics on the dm-dimensional simplex. This estimator, being an extension of the univariate beta kernel estimator, effectively addressed boundary biases. Our analysis established its asymptotic normality and uniform strong consistency. Additionally, we introduced a beta kernel estimator specifically tailored for conditional U-statistics, demonstrating both weak and strong uniform convergence. Our investigation considered the expansion of compact sets and various sequences of smoothing parameters. For the first time, we examined conditional U-statistics based on mixed categorical and continuous regressors. We presented new findings on conditional U-statistics smoothed by multivariate Bernstein kernels, previously unexplored in the literature. These results are derived under sufficiently broad conditions on the underlying distributions. The main ingredients used in our proof were truncation methods and sharp exponential inequalities tailored to the U-statistics in connection with the empirical processes theory. Our theoretical advancements significantly contributed to the field of asymmetric kernel estimation, with potential applications in areas such as discrimination problems, ℓ-sample conditional U-statistics, and the Kendall rank correlation coefficient. Finally, we conducted some simulations to demonstrate the small sample performances of the estimators. [ABSTRACT FROM AUTHOR]