In this paper, we investigate the complete convergence for weighted sums of widely orthant-dependent (WOD, for short) random variables. Our results extend the corresponding ones of Chen and Sung (Stat Probab Lett 154,...
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In this paper, we investigate the complete convergence for weighted sums of widely orthant-dependent (WOD, for short) random variables. Our results extend the corresponding ones of Chen and Sung (Stat Probab Lett 154, 2019) to a much more general type of complete convergence. As an application of our main results, we establish the complete consistency for the estimator in the nonparametric regression models and provide a simulation study to assess the finite sample performance of the theoretical results.
Consider the following nonparametric regression model:where x(ni) are known fixed design points from for some positive integer d > 1, g( center dot ) is an unknown regression function defined on A and epsilon(ni) a...
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Consider the following nonparametric regression model:where x(ni) are known fixed design points from for some positive integer d > 1, g( center dot ) is an unknown regression function defined on A and epsilon(ni) are random errors. Under some suitable conditions, the asymptotic normality of the linear weighted estimator of g in the nonparametric regression model based on rho-mixing errors is established. The key techniques used in the paper are the Rosenthal type inequality and the Bernstein's bigblock and small-block procedure. The result obtained in the paper generalizes the corresponding ones for some dependent sequences.
To address the curse of dimensionality problem associated with multivariate nonparametric regression models, we consider partially linear regressionmodels. A contribution to statistical inference in the partially lin...
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To address the curse of dimensionality problem associated with multivariate nonparametric regression models, we consider partially linear regressionmodels. A contribution to statistical inference in the partially linear regressionmodel is to propose estimators of the error variance with good asymptotic properties. We propose two estimators of the error variance in a partially linear regressionmodel and their respective asymptotic normality. Using a simulation–based study, we will compare the performance of our estimator with the performance of other concurrent estimators existing in the statistical literature. Pour pallier le problème de la malédiction de la dimension lié au modèle de régression non paramétrique, les modèles de régressions partiellement linéaires, lorsque les données s'y prêtent sont utilisés. Une des contributions à l'inférence statistique dans le modèle de régression partiellement linéaire est de proposer des estimateurs de la variance des erreurs ayant de bonnes propriétés asymptotiques. Dans cet article nous proposerons deux estimateurs de la variance des erreurs dans un modèle de régression partiellement linéaire ainsi que leurs normalités asymptotiques respectives. À l'aide de simulations nous comparerons les performances de nos estimateurs par rapport aux performances d'autres estimateurs concurrents existant dans la littérature statistique.
In this paper, we mainly study the asymptotic properties of weighted estimator for the nonparametric regression model based on linearly negative quadrant dependent (LNQD, for short) errors. We obtain the rate of unifo...
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In this paper, we mainly study the asymptotic properties of weighted estimator for the nonparametric regression model based on linearly negative quadrant dependent (LNQD, for short) errors. We obtain the rate of uniformly asymptotic normality of the weighted estimator which is nearly O(n(-1/4)) when the moment condition is appropriate. The results generalize the corresponding ones of Yang (2003) from NA samples to LNQD samples and improve or extend the corresponding one of Li et al. (2012) for LNQD samples. Moreover, we obtain some results on mean consistency, uniformly mean consistency, and the rate of mean consistency for the weighted estimator. Finally we carry out some simulations to verify the validity of our results. (C) 2019 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
In this paper, we present theLp documentclass convergence for partial sumsSn=n-ary sumation k=1nXk documentclass under the Cesaro uniform integrability condition and the complete convergence for the maximum ofSn\docum...
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In this paper, we present theLp documentclass convergence for partial sumsSn=n-ary sumation k=1nXk documentclass under the Cesaro uniform integrability condition and the complete convergence for the maximum ofSn\documentclass for sequences of widely orthant dependent random variables Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.
In this paper, we mainly studied the complete convergence for weighted sums of widely negative orthant dependent (WNOD, in short) random variables. Some sufficient conditions to prove the complete convergence are prov...
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In this paper, we mainly studied the complete convergence for weighted sums of widely negative orthant dependent (WNOD, in short) random variables. Some sufficient conditions to prove the complete convergence are provided. As an application, the complete consistency for the weighted estimator of nonparametric regression model is established, and the simulation study is provided to evaluate the finite sample performance of the consistency for the nearest neighbour weight function estimator.
In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete ...
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In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete moment and complete convergences for the variables. As applications, the complete consistency for the estimators of nonparametric and semiparametric regressionmodels based on negatively orthant dependent errors is established by using the complete convergence that we established. A simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimator in semiparametric regressionmodel is given. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.
In this paper, we will study the complete and complete moment convergence for double-indexed randomly weighted sums of rho*-mixing random variables. Several sufficient conditions to prove the complete and complete mom...
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In this paper, we will study the complete and complete moment convergence for double-indexed randomly weighted sums of rho*-mixing random variables. Several sufficient conditions to prove the complete and complete moment convergence for randomly weighted sums of rho*-mixing random variables are presented. The results obtained in this paper extend some corresponding ones in the literature. As applications, we further study the convergence of the state observers of linear-time-invariant systems and the complete consistency for the weighted estimator in nonparametric regression models based on rho*-mixing random errors. Finally, some numerical simulations are provided to verify the validity of theoretical results.
Consider the wavelet estimator of a nonparametric regression model with repeated measurements under martingale difference error's structure for exhibiting dependence among the units, and to avoid as far as possibl...
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Consider the wavelet estimator of a nonparametric regression model with repeated measurements under martingale difference error's structure for exhibiting dependence among the units, and to avoid as far as possible any assumptions among the observations within the same unit. We show the moment consistency, the strong consistency and the strong convergence rate of the wavelet estimator, and establish its asymptotic normality. (C) 2012 Elsevier B.V. All rights reserved.
作者：
Wang, DabuxilatuGuangzhou Univ
Higher Educ Mega Ctr Dept Stat 230 Waihuanxi Rd Guangzhou 510006 Guangdong Peoples R China
A linearity test for a multiple regressionmodel with LR-fuzzy responses and LR-fuzzy explanatory variables is considered. The regressionmodel consists of severalmultiple regressionmodels from response center or spr...
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ISBN:
(纸本)9783319429724;9783319429717
A linearity test for a multiple regressionmodel with LR-fuzzy responses and LR-fuzzy explanatory variables is considered. The regressionmodel consists of severalmultiple regressionmodels from response center or spreads to the explanatory centers and spreads. A multiple nonparametric regression model to be employed as a reference in the testing approach is estimated, and with which the linearity of the regressionmodel is tested. Some simulation example is also presented.
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