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Based on the approach of left and right kernel smoothing with unilateral kernel function, we, in this paper, define estimators of change point and jump size in nonparametric regression model with r...

In this paper, we focus on the partially linear varying-coefficient quantile regression model with observations missing at random (MAR), which include the responses or the responses and covariates ...

In this paper, we focus on the left-truncated and right-censored model, and construct the local linear and Nadaraya-Watson type estimators of the conditional density. Under suitable conditions, we ...

Based on the inverse probability weight method, we, in this article, construct the empirical likelihood (EL) and penalized empirical likelihood (PEL) ratios of the parameter in the linear quantile ...

In order to investigate the convergence rate of the asymptotic normality for the estimator of the conditional mode function for the left-truncation model, we derive a Berry–Esseen type bound of the estimator when the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The finite sample performance of the estimator of the conditional mode function is explored through simulations.

In this article, we study global L2 error of non linear wavelet estimator of density in the Besov space Bspq for missing data model when covariables are present and prove that the estimator can achieve the optimal rate of convergence, which is similar to the result studied by Donoho et al. (1996) in complete independent data case with term-by-term thresholding of the empirical wavelet coefficients. Finite-sample behavior of the proposed estimator is explored via simulations.

Consider the heteroscedastic partially linear errors-in-variables (EV) model yi = xiβ + g(ti) + ei, ξi = xi + μi (1 ⩽ i ⩽ n), where ei = σiei are random errors with mean zero, σ2i = f(ui), (xi, ti, ui) are non random design points, xi are observed with measurement errors μi. When f( · ) is known, we derive the Berry–Esseen type bounds for estimators of β and g( · ) under {ei, 1 ⩽ i ⩽ n} is a sequence of stationary α-mixing random variables, when f( · ) is unknown, the Berry–Esseen type bounds for estimators of β, g( · ), and f( · ) are discussed under independent errors.

Consider the heteroscedastic semi-parametric model y i = x i β +g(t i ) + σ i e i (1 ≤ i ≤ n), where , the design points (x i , t i , u i ) are known and non random, g(·) and f(·) are unknown functions defined on closed interval [0, 1], and the random errors e i are assumed to be a sequence of stationary α-mixing random variables with mean zero. Under appropriate conditions, we study the asymptotic normality of least-squares estimator and two weighted least-squares estimators of β. Also, the asymptotic normality of the estimators of g(·) and f(·) is considered. Finite sample behavior of the estimators is investigated via simulations as well.

The purpose of this article is to use the empirical likelihood method to study construction of the confidence region for the parameter of interest in heteroscedastic partially linear errors-in-variables model with martingale difference errors. When the variance functions of the errors are known or unknown, we propose the empirical log-likelihood ratio statistics for the parameter of interest. For each case, a nonparametric version of Wilks’ theorem is derived. The results are then used to construct confidence regions of the parameter. A simulation study is carried out to assess the performance of the empirical likelihood method.

In this article, we establish strong uniform convergence and asymptotic normality of estimators of conditional quantile and conditional distribution function for a left truncated model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary α-mixing sequence. The results of Lemdani et al. (2009) are relaxed from the i.i.d. assumption to α-mixing setting. Finite sample behavior of the estimators is investigated via simulations as well.

In this article we establish pointwise asymptotic normality of nonparametric kernel estimator of regression function for a left truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the asymptotic normality of the estimation of the covariable's density is considered. As a by-product, we obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and truncated distributions under dependence, which is interesting independently. Finite sample behavior of the estimator of the regression function is investigated as well.

Consider the heteroscedastic regression model , where , β is a p × 1 column vector of unknown parameter, (X i , T i , Z i ) are random design points, Y i are the response variables, g(·) is an unknown function defined on the closed interval [0, 1], {e i , ℱ i } is a sequence of martingale differences. When f is known and unknown cases, we propose the empirical log-likelihood ratio statistics for the parameter β. For each case, a nonparametric version of Wilks' theorem is derived. The results are then used to construct confidence regions of the parameter. Simulation study shows that the empirical likelihood method performs better than a normal approximation-based approach.

In this article, we employ the method of empirical likelihood to construct confidence intervals of conditional density for a left-truncation model. It is proved that the empirical likelihood ratio admits a limiting chi-square distribution with one degree of freedom when the lifetime observations with multivariate covariates form a stationary α-mixing sequence.

In this article, we study the consistency of the error density estimator in nonparametric regression models when the errors form a stationary α-mixing sequences. These results improve the results of Cheng (2004) from the i.i.d. assumption to α-mixing condition and weaken the restrictions for the bandwidths a n . Also, the rates of strong convergence for the estimator are investigated. Furthermore, we derive the asymptotic normality and the law of the iterated logarithm of the histogram-type error density estimator, which complement the conclusion in Cheng (2002) in α-mixing setting.