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In recent years, the direction has turned to non-stationary time series. Here the situation is more complicated: it is often unclear how to set down a meaningful asymptotic for non-stationary processes. For this reason, the theory of locally stationary processes arose, and it is based on infill asymptotics created from non-parametric statistics. The present paper aims to develop a framework for inference of locally stationary functional time series based on the so-called conditional U-statistics introduced by Stute (Ann Probab 19:812–825, 1991), and may be viewed as a generalization of the Nadaraya-Watson regression function estimates. In this paper, we introduce an estimator of the conditional U-statistics operator that takes into account the nonstationary behavior of the data-generating process. We are mainly interested in establishing weak convergence of conditional U-processes in the locally stationary functional mixing data framework. More precisely, we investigate the weak convergence of conditional U-processes when the explicative variable is functional. We treat the weak convergence when the class of functions is bounded or unbounded, satisfying some moment conditions. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The theoretical results established in this paper are (or will be) critical tools for further functional data analysis developments. [ABSTRACT FROM AUTHOR]

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained. [ABSTRACT FROM AUTHOR]

This paper proposes nonparametric estimators for extropy-related measures based on the famous Kaplan–Meier estimator and the kernel density estimator for right censored data. Properties such as consistency and asymptotic normality of the proposed kernel estimators under the dependence condition are established. Moreover, the performance of the suggested estimators is evaluated using both simulated and real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an approximation for the distribution function of sum of two independent random variables using quantile based representation. The error of approximation is shown to be negligible under some mild conditions. We then use the approximation to obtain a non-parametric estimator for the distribution function of sum of two independent random variables. The exact distribution of the proposed estimator is derived. The estimator is shown to be strongly consistent and asymptotically normally distributed. Extensive Monte Carlo simulation studies are carried out to evaluate the bias and mean squared error of the estimator and also to assess the approximation error. We also compare the performance of the proposed estimator with other estimators available in the literature. Finally, we illustrate the use of the proposed estimator for estimating the reliability function of a standby redundant system. [ABSTRACT FROM AUTHOR]

In this paper, we study spatial cross-sectional data models in the form of matrix exponential spatial specification (MESS), where MESS appears in both dependent and error terms. The empirical likelihood (EL) ratio statistics are established for the parameters of the MESS model. It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions, which are used to construct the confidence regions of model parameters. Simulation experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method. [ABSTRACT FROM AUTHOR]

This paper studies the statistical query (SQ) complexity of estimating d-dimensional submanifolds in R n . We propose a purely geometric algorithm called manifold propagation, that reduces the problem to three natural geometric routines: projection, tangent space estimation, and point detection. We then provide constructions of these geometric routines in the SQ framework. Given an adversarial STAT (τ) oracle and a target Hausdorff distance precision ε = Ω (τ 2 / (d + 1)) , the resulting SQ manifold reconstruction algorithm has query complexity O ~ (n ε - d / 2) , which is proved to be nearly optimal. In the process, we establish low-rank matrix completion results for SQ's and lower bounds for randomized SQ estimators in general metric spaces. [ABSTRACT FROM AUTHOR]

Survival causal effect estimation based on right-censored data is of key interest in both survival analysis and causal inference. Propensity score weighting is one of the most popular methods in the literature. However, since it involves the inverse of propensity score estimates, its practical performance may be very unstable, especially when the covariate overlap is limited between treatment and control groups. To address this problem, a covariate balancing method is developed in this paper to estimate the counterfactual survival function. The proposed method is nonparametric and balances covariates in a reproducing kernel Hilbert space (RKHS) via weights that are counterparts of inverse propensity scores. The uniform rate of convergence for the proposed estimator is shown to be the same as that for the classical Kaplan–Meier estimator. The appealing practical performance of the proposed method is demonstrated by a simulation study as well as two real data applications to study the causal effect of smoking on survival time of stroke patients and that of endotoxin on survival time for female patients with lung cancer respectively. [ABSTRACT FROM AUTHOR]

In this paper, we study some asymptotic properties for the Bernstein estimators of the limit distribution function and the limit density function under a triangular sample. Specifically, we obtain the uniform strong consistency, mean squared error (MSE) and mean integrated squared error (MISE) for the resulting estimators. In addition, we give the optimal choice of the bandwidth parameter m in terms of the sample size n, for both the MSE and MISE. Numerical simulations are presented to show that the Bernstein estimators outperform Gaussian kernel estimators in terms of MISE under a triangular sample. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. W. Stute [Ann. Probab. 19 (1991) 812–825] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to : m (t) : = E [ φ (Y 1 , ... , Y m) | (X 1 , ... , X m) = t ] , for t ∈ X m. In this paper we are mainly interested in establishing weak convergence of conditional U-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of conditional U-processes when the explicative variable is functional. We treat the weak convergence in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for many further developments in functional data analysis. [ABSTRACT FROM AUTHOR]

In this paper, we study nonparametric local linear estimation of the conditional density of a randomly censored scalar response variable given a functional random covariate. We establish under general conditions the pointwise almost sure convergence with rates of this estimator under α -mixing dependence. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning Kidney transplant data. [ABSTRACT FROM AUTHOR]

In this paper, we estimate the conditional cumulative distribution function of a randomly censored scalar response variable given a functional random variable using the local linear approach. Under this structure, we state the asymptotic normality with explicit rates of the constructed estimator. Moreover, the usefulness of our results is illustrated through a simulated study. [ABSTRACT FROM AUTHOR]

This paper deals with a projection least squares estimator of the function J 0 computed from multiple independent observations on [ 0 , T ] of the process Z defined by d Z t = J 0 (t) d 〈 M 〉 t + d M t , where M is a continuous square-integrable martingale vanishing at 0. Risk bounds are established for this estimator, an associated adaptive estimator and an associated discrete-time version used in practice. An appropriate transformation allows us to rewrite the differential equation d X t = V (X t) (b 0 (t) d t + σ (t) d B t) , where B is a fractional Brownian motion with Hurst parameter H ∈ [ 1 / 2 , 1) , as a model of the previous type. The second part of the paper deals with risk bounds for a nonparametric estimator of b 0 derived from the results on the projection least squares estimator of J 0 . In particular, our results apply to the estimation of the drift function in a non-autonomous Black–Scholes model and to nonparametric estimation in a non-autonomous fractional stochastic volatility model. [ABSTRACT FROM AUTHOR]

For at least the last two decades, diversification has been an important issue in the strategic management research. This paper explores how diversification affects the corporate performance of the top 100 manufacturing companies in Taiwan, which were selected based on a ranking survey of Taiwanese manufacturing firms conducted by Common Wealth Magazine in 2014. This paper adopts a dynamic data envelopment analysis model to estimate efficiency in the first stage, and adopts OLS regression analysis in the second stage from 2009 to 2013. Two proxies, namely the Entropy approach and the Herfindahl-Hirschman Index, are used to proxy for diversification. The results indicate that diversification has positive impacts on dynamic efficiency, after controlling firm-specific factors. Concisely, this study empirically proves that diversification is an important corporate strategy for improving corporate performance over long-term periods. Overall, “putting eggs in various baskets” enable companies to not only survive, but also sustain competitive advantage in today’s challenging business world. [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]

Bifurcating Markov chains are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistency and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the distinction of the three regimes on the ergodic rate identified in a previous work (for fluctuations of average over large generations) disappears. This result is a first step to go beyond the threshold condition on the ergodic rate given in previous statistical papers on functional estimation. [ABSTRACT FROM AUTHOR]

In this paper, we establish the complete convergence of the weighted sums for martingale differences, which is the interesting supplements for some known results. As statistical applications, when errors are martingale differences, the least square estimator in the errors-in-variables regression model and the regression function estimator in nonparametric regression model are studied and their strong consistency is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete moment convergence for randomly weighted sums of extended negatively dependent (END) random variables. The results obtained in this paper extended the corresponding one of Li et al. (J Inequalities Appl 2017:16, 2017). As an application, we study the complete consistency for the estimator of semiparametric regression models based on END random variables by using the complete convergence that we established. Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results. [ABSTRACT FROM AUTHOR]

In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the Wasserstein distance, which allows to set forth an interesting connection between PCRs and some classical problems arising in mathematical analysis, probability and statistics, e.g., Laplace methods for approximating integrals, Sanov's large deviation principles in the Wasserstein distance, rates of convergence of mean Glivenko–Cantelli theorems, and estimates of weighted Poincaré–Wirtinger constants. We first present a theorem on PCRs for a model in the regular infinite-dimensional exponential family, which exploits sufficient statistics of the model, and then extend such a theorem to a general dominated model. These results rely on the development of novel techniques to evaluate Laplace integrals and weighted Poincaré–Wirtinger constants in infinite-dimension, which are of independent interest. The proposed approach is applied to the regular parametric model, the multinomial model, the finite-dimensional and the infinite-dimensional logistic-Gaussian model and the infinite-dimensional linear regression. In general, our approach leads to optimal PCRs in finite-dimensional models, whereas for infinite-dimensional models it is shown explicitly how the prior distribution affect PCRs. [ABSTRACT FROM AUTHOR]

In this paper, the Bahadur representation of the empirical and Bernstein polynomials estimators of the quantile function based on associated sequences are investigated. The rate of approximation depends on the rate of decay in covariances, and it converges to the optimal rate observed under independence when the covariances quickly approach zero. As an application, we establish a Berry-Esseen bound with the rate O (n - 1 / 3) assuming polynomial decay of covariances. All these results are established under fairly general conditions on the underlying distributions. Additionally, we perform Monte Carlo simulations to evaluate the finite sample performance of the suggested estimators, utilizing an associated and non-mixing model. [ABSTRACT FROM AUTHOR]

The proportional odds (PO) model is one of the most commonly used models for regression analysis of failure time data in survival analysis. It assumes that the odds of the failure is proportional to the baseline odds at any point in time given the covariate. The model focus on the situation that the ratio of the hazards converges to unity as time goes to infinity, while the proportional hazards (PH) model has a constant ratio of hazards over time. In the paper, we consider a general type of failure time data, case K interval-censored data, that include case I or case II interval-censored data as special cases. We propose a PO model-based unified penalized variable selection procedure that involves minimizing a negative sieve log-likelihood function plus a broken adaptive ridge penalty, with the initial values obtained from the ridge regression estimator. The proposed approach allows dependent censoring, which occurs quite often and could lead to biased or misleading estimates without considering it. We show that the proposed selection method has oracle properties and the estimator is semiparametrically efficient. The numerical studies suggest that the proposed approach works well for practical situations. In addition, the method is applied to an ADNI study that motivates this investigation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial linear regression model yi = xiβ* + g(ti) + εi, i = 1, 2, ..., n, where (xi, ti) are known fixed design points, g(·) is an unknown function, and β* is an unknown parameter to be estimated, random errors εi are (α, β)-mixing random variables. The p-th (p > 1) mean consistency, strong consistency and complete consistency for least squares estimators of β* and g(·) are investigated under some mild conditions. In addition, a numerical simulation is carried out to study the finite sample performance of the theoretical results. Finally, a real data analysis is provided to further verify the effect of the model. [ABSTRACT FROM AUTHOR]

In this paper, we develop Jajte's technique, which is used in the proof of strong laws of large numbers, to prove complete convergence for randomly weighted sums of negatively associated random variables. Based on a general normalizing function that satisfies some specific conditions, we give some general results on complete convergence for randomly weighted sums of random variables. The Baum–Katz theorem for randomly weighted sums with general normalizing sequences is also presented. Our results have an interesting connection with the theory of regularly varying functions. These results are applied to simple linear regression models as well as nonparametric regression models with random design. Furthermore, simulations to study the numerical performance of the consistency for nearest neighbor weight function estimators in nonparametric regression and least-squares estimators in a simple linear regression with random design are given. [ABSTRACT FROM AUTHOR]

Conventional higher-order spatial autoregressive models assume that all regression coefficients are constant, which ignores dynamic feature that may exist in spatial data. In this paper, we introduce a semiparametric dynamic higher-order spatial autoregressive model by allowing regression coefficients in classical higher-order spatial autoregressive models to smoothly vary with a continuous explanatory variable, which enables us to explore dynamic feature in spatial data. We develop a sieve two-stage least squares method for the proposed model and derive asymptotic properties of resulting estimators. Furthermore, we develop two testing methods to check appropriateness of certain linear constraint condition on the spatial lag parameters and stationarity of the regression relationship, respectively. Simulation studies show that the proposed estimation and testing methods perform quite well in finite samples. The Boston house price data are finally analyzed to demonstrate the proposed model and its estimation and testing methods. [ABSTRACT FROM AUTHOR]

The present paper deals with the problem of nonparametric estimation of the trend for stochastic processes driven by G-Brownian motion with small noise. The consistency, the bound on the rate of convergence, and the asymptotic distribution of the nonparametric estimator are studied. Finally, a numerical example is given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

Let J 1 > J 2 > ⋯ be the ranked jumps of a gamma process τ α on the time interval [ 0 , α ] , such that τ α = ∑ k = 1 ∞ J k . In this paper, we design an algorithm that samples from the random vector (J 1 , ⋯ , J N , ∑ k = N + 1 ∞ J k) . Our algorithm provides an analog to the well-established inverse Lévy measure (ILM) algorithm by replacing the numerical inversion of exponential integral with an acceptance-rejection step. This research is motivated by the construction of Dirichlet process prior in Bayesian nonparametric statistics. The prior assigns weight to each atom according to a GEM distribution, and the simulation algorithm enables us to sample from the N largest random weights of the prior. Then we extend the simulation algorithm to a generalised gamma process. The simulation problem of inhomogeneous processes will also be considered. Numerical implementations are provided to illustrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we develop a flexible semiparametric model averaging marginal regression procedure to forecast the joint conditional quantile function of the response variable for ultrahigh-dimensional data. First, we approximate the joint conditional quantile function by a weighted average of one-dimensional marginal conditional quantile functions that have varying coefficient structures. Then, a local linear regression technique is employed to derive the consistent estimates of marginal conditional quantile functions. Second, based on estimated marginal conditional quantile functions, we estimate and select the significant model weights involved in the approximation by a nonconvex penalized quantile regression. Under some relaxed conditions, we establish the asymptotic properties for the nonparametric kernel estimators and oracle estimators of the model averaging weights. We further derive the oracle property for the proposed nonconvex penalized model averaging procedure. Finally, simulation studies and a real data analysis are conducted to illustrate the merits of our proposed model averaging method. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the k-Nearest Neighbors (k-NN) method in the single index regression model in the case of a functional predictor and a scalar response. The main result of this work is the establishment of the almost complete convergence rates for the quasi-associated data. The obtained results rely on the classical functional kernel estimate. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator. Finally, we show how to use the k-NN estimator of the functional single index regression model in the analysis of air quality to illustrate the effectiveness of our methodology. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained. [ABSTRACT FROM AUTHOR]

It is well known that the empirical distribution function has superior properties as an estimator of the underlying distribution function F. However, considering its jump discontinuities, the estimator is limited when F is continuous. Mixtures of the binomial probabilities relying on Bernstein polynomials lead to good approximation properties for the resulting estimator of F. In this paper, we establish the rates of (pointwise) asymptotic normality for Bernstein estimators by the Berry-Esseen Theorem in the case that the observations are in a triangular array. Particularly, the (asymptotic) absence of the boundary bias and the asymptotic behaviors of the variance are investigated. Besides, numerical simulations are presented to verify the validity of our main results. [ABSTRACT FROM AUTHOR]

Nonparametric estimation for a large-sized sample subject to sampling bias is studied in this paper. The general parameter considered is the mean of a transformation of the random variable of interest. When ignoring the biasing weight function, a small-sized simple random sample of the real population is assumed to be additionally observed. A new nonparametric estimator that incorporates kernel density estimation is proposed. Asymptotic properties for this estimator are obtained under suitable limit conditions on the small and the large sample sizes and standard and non-standard asymptotic conditions on the two bandwidths. Explicit formulas are shown for the particular case of mean estimation. Simulation results show that the new mean estimator outperforms two classical ones for suitable choices of the two smoothing parameters involved. The influence of two smoothing parameters on the performance of the final estimator is also studied, exhibiting a striking limit behavior of their optimal values. The new method is applied to a real data set from the Telco Company Vodafone ES, where a bootstrap algorithm is used to select the smoothing parameter. [ABSTRACT FROM AUTHOR]

In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O (n − 1 / 3) under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the nonparametric regression model with random design based on (X t , Y t) t ≥ 0 a R d × R q -valued strictly stationary and ergodic continuous time process, where the regression function is given by m (x , ψ) = E (ψ (Y) ∣ X = x)) , for a measurable function ψ : R q → R . We focus on the estimation of the location Θ (mode) of a unique maximum of m (· , ψ) by the location Θ ^ T of a maximum of the Nadaraya–Watson kernel estimator m ^ T (· , ψ) for the curve m (· , ψ) . Within this context, we obtain the consistency with rate and the asymptotic normality results for Θ ^ T under mild local smoothness assumptions on m (· , ψ) and the design density f (·) of X . Beyond ergodicity, any other assumption is imposed on the data. This paper extends the scope of some previous results established under the mixing condition. The usefulness of our results will be illustrated in the construction of confidence regions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new estimation method for a nonparametric hidden Markov model (HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization (EM) algorithm is developed to compute the maximum composite likelihood. We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk's phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange (CBOE) are conducted to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The measure of entropy has a pivotal role in the information theory area. In this paper, estimation of differential entropy for Pareto distribution in presence of r outliers is considered. In this regard, the classical and Bayesian estimation techniques of differential entropy are employed. In classical setup, we obtain the maximum likelihood estimators of the differential entropy as well as assessing their performance via a simulation study. The entropy Bayesian estimator is derived using squared error, linear exponential, weighted squared error and K loss functions. The Metropolis-Hastings algorithm is used to generate posterior random variables. Monte Carlo simulations are designed to implement the precision of estimates for different sample sizes and number of outliers. Furthermore, performance of estimates is planned by experiments with real data. Generally, we conclude that the entropy Bayesian estimates of simulated data tend to the true value as the number of outliers increases. Further, the entropy Bayesian estimate under weighted squared error loss function is preferable to the other estimates in majority of situations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the confidence interval construction for the partially nonlinear models with missing responses at random under the framework of quantile regression. We propose an imputation-based empirical likelihood method to construct statistical inferences for both the unknown parametric vector in the nonlinear function and the nonparametric function and show that the proposed empirical log-likelihood ratios are both asymptotically chi-squared in theory. Furthermore, the confidence region for the parametric vector and the pointwise confidence interval for the nonparametric function are constructed. Some simulation studies are implemented to assess the performances of the proposed estimation method, and simulation results indicate that the proposed method is workable. [ABSTRACT FROM AUTHOR]

In this paper the problem of one dimensional parameter estimation is considered in the case where observations are coming from inhomogeneous Poisson processes. The method of moments estimation is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of the estimator and the expansion of the distribution function. The stochastic expansion, the expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we study a high dimension (Big Data) regression model in continuous time observed in the discrete time moments with dependent noises defined by semimartingale processes. To this end an improved (shrinkage) estimation method is developed and the non-asymptotic comparison between shrinkage and least squares estimates is studied. The improvement effect for the shrinkage estimates showing the significant advantage with respect to the "small" dimension case is established. It turns out that obtained improvement effect holds true uniformly over observation frequency. Then, a model selection method based on these estimates is developed. Non-asymptotic sharp oracle inequalities for the constructed model selection procedure are obtained. Constructive sufficient conditions for the observation frequency providing the robust efficiency property in adaptive setting without using any sparsity assumption are found. A special stochastic calculus tool to guarantee these conditions for non-Gaussian Ornstein–Uhlenbeck processes is developed. Monte-Carlo simulations for the numeric confirmation of the obtained theoretical results are given. [ABSTRACT FROM AUTHOR]

For the semiparametric regression model: Y(j)(xin,tin)=tinβ+g(xin)+e(j)(xin),1≤j≤m,1≤i≤n, where tin∈R and xin∈Rp are known to be nonrandom, g is an unknown continuous function on a compact set A in Rp, ej(xin) are ρ∗-mixing random errors with mean zero, Y(j)(xin,tin) represent the j-th response variables which are observable at points xin,tin. In this paper, we study the strong consistency and r-th (1) mean consistency for the estimators βm,n and gm,n of β and g, respectively. The results obtained in this paper improve and extend the corresponding ones for ρ∗-mixing random variables and other dependent sequences. [ABSTRACT FROM AUTHOR]

In the paper, the Marcinkiewicz-Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the $$L_r$$ convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated by using the Marcinkiewicz-Zygmund type moment inequality. In addition, some applications of the $$L_r$$ convergence, weak and strong laws of large numbers to nonparametric regression models based on END errors are provided. The results obtained in the paper generalize or improve some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g(x) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972). Finally, we present a numerical simulation study to verify the validity of the results established here. [ABSTRACT FROM AUTHOR]

This paper describes a method for estimation and inference with a nonparametric varying coefficients panel data model that allows for cross-sectional dependence and heteroscedasticity, wherein the time series length T is larger than the cross-sectional size N. We first eliminate fixed effects by taking the cross-sectional average, and then use a local linear approach to obtain the initial estimator of the unknown coefficient functions. However, the initial estimator ignores the cross-sectional dependence and heteroscedasticity, which will lead to a loss of efficiency. Thus, we propose a weighted local linear method to obtain a more efficient estimator. In the theoretical part of the paper, we derive the asymptotic theory of the resulting estimator. Simulation results and a real data analysis are provided to illustrate the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on φ -mixing random variables. The rth mean consistency, complete consistency, uniform rth mean consistency and uniform complete consistency are established under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency of the nearest neighbor weight function estimators is provided. The results obtained in the paper improve the conditions in the literature and generalize the existing results of independent random errors to the case of φ -mixing random errors. [ABSTRACT FROM AUTHOR]

As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort. Simulation studies elucidate the practical performance of the proposed method under finite samples. As an illustration, we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonparametric estimator of the regression function based on the local linear estimation method in a twice censoring setting. The proposed method avoid the problem of boundary effect and reduces the bias term. Under suitable assumptions, the strong uniform almost sure consistency with rate is established and the finite sample properties of the local linear regression smoother is investigated by means of a simulation study. [ABSTRACT FROM AUTHOR]

Let X, Y, W, δ and ε be continuous univariate random variables defined on a probability space such that Y = X + ε and W = X + δ . Herein X, δ and ε are assumed to be mutually independent. The variables ε and δ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample Y 1 , ... , Y n from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function F W of W based on the observations as well as on the distributions of ε , δ . An estimator for F W depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, δ and ε , we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The ℓ 1 trend filtering enables us to estimate a continuous piecewise linear trend of univariate time series. This filter and its variants have subsequently been applied in various fields, including astronomy, climatology, economics, electronics, environmental science, finance, and geophysics. Although the ℓ 1 trend filtering can estimate a continuous piecewise linear trend of univariate time series, it cannot estimate a common continuous piecewise linear trend of multiple time series. This paper develops a statistical procedure that enables us to estimate it, which is a multivariate extension of the ℓ 1 trend filtering. We provide an algorithm for estimating it and a clue to specify the tuning parameter of the procedure, both required for its application. We also (i) numerically illustrate how well the algorithm works, (ii) provide an empirical illustration, and (iii) introduce a generalization of our novel method. [ABSTRACT FROM AUTHOR]

The reach of a submanifold is a crucial regularity parameter for manifold learning and geometric inference from point clouds. This paper relates the reach of a submanifold to its convexity defect function. Using the stability properties of convexity defect functions, along with some new bounds and the recent submanifold estimator of Aamari and Levrard (Ann. Statist. 47(1), 177–204 (2019)), an estimator for the reach is given. A uniform expected loss bound over a C k model is found. Lower bounds for the minimax rate for estimating the reach over these models are also provided. The estimator almost achieves these rates in the C 3 and C 4 cases, with a gap given by a logarithmic factor. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new non-parametric test for equality of distributions. The test is based on the recently introduced measure of (niche) overlap and its rank-based estimator. As the estimator makes only one basic assumption on the underlying distribution, namely continuity, the test is universal applicable in contrast to many tests that are restricted to only specific scenarios. By construction, the new test is capable of detecting differences in location and scale. It thus complements the large class of rank-based tests that are constructed based on the non-parametric relative effect. In simulations this new test procedure obtained higher power and lower type I error compared to two common tests in several settings. The new procedure shows overall good performance. Together with its simplicity, this test can be used broadly. [ABSTRACT FROM AUTHOR]

Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors, the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments (GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones. [ABSTRACT FROM AUTHOR]