Convergence Rate of Estimator forNonparametric Regression Model under ρ-mixing Errors

In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.

Expanded Barro Regression in Studying Convergence Problem

This study develops the approach by Minh & Khanh [1] to the classic Barro and Sala-i-Martin method [2], [3] named “expanded Barro regression method”, and applies this approach in analyzing the convergence of provincial per capita GDP in Vietnam over the period of 1991-2007. Different aspects of provincial convergence are considered in this paper. The estimated result on conver-gence from our model is compared to other models.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

Carbon productivity convergence club and its initial conditions: China's construction industry

A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial difference. The second stage is to identify the convergence club of DCP. The last stage is to examine the initial factors that may affect the formation of the convergence club. Construction industry data from 30 provinces in China's Mainland from 2005 to 2016 were adopted to conduct an empirical study. The empirical results showed that (1) the arithmetic mean value of China’s provincial DCP showed an upward trend and the standard deviation showed an expanding trend.(2) There are five convergence clubs, but 13 provinces failed to converge to any club.(3) The higher the degree of construction industry marketization in 2005, the greater the probability that the provinces belong to a club with higher DCP. To improve the DCP, the effective diffusion of low-carbon construction technologies and the market-oriented reform of state-owned construction companies should be promoted. The three-stage method can also be applied to study different industries in different countries or regions.

Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples

Consider the following heteroscedastic semiparametric regression model: y_i = Xi T β + g(ti) + σiei, 1 ≤ i ≤ n, where {Xi, 1 ≤ i ≤ n} are random design points, errors {ei, 1 ≤ i ≤ n} are negatively associated (NA) random variables, σi2 = h(ui), and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g(t) and the variance function h(u) are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O(n^(-1/3) log n). Hence our results are extensions of those results on independent random error settings.

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.

Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors

Consider the partly linear regression model , where y i ’s are responses, are known and nonrandom design points, is a compact set in the real line , β = (β 1, ··· , β p )' is an unknown parameter vector, g(·) is an unknown function and {ε i } is a linear process, i.e., , where e j are i.i.d. random variables with zero mean and variance . Drawing upon B-spline estimation of g(·) and least squares estimation of β, we construct estimators of the autocovariances of {ε i }. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {ε i } are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.

Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.

非线性模型的众数回归估计

在应用众数回归方法来考虑非线性模型的估计时,把调整参数当作常数,在适当的条件下得到估计量的√n收敛速度,改进了已有的众数回归估计方法,即把调整参数作为变量.最后,通过一定数量的模拟实验来验证众数回归估计的稳健性.

NSD随机阵列最大加权和的矩收敛性及应用

该文利用NSD随机阵列的极大值矩不等式研究了NSD随机阵列最大加权和的矩收敛性,相关定理改进且推广了已有关于AANA变量的结果 .此外,作为主要结果的应用,进一步研究了非参数回归模型加权估计量的矩相合性和弱相合性.

Bootstrap Approximation of Wavelet Estimates in a Semiparametric Regression Model

The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.

Asymptotic Properties of Wavelet Estimators in a Semiparametric Regression Model with Censored Data

Consider a semiparametric regression model Y_i=X_iβ＋g（t_i）＋e_i, 1 ≤ i ≤ n, where Y_i is censored on the right by another random variable C_i with known or unknown distribution G. The wavelet estimators of parameter and nonparametric part are given by the wavelet smoothing and the synthetic data methods. Under general conditions, the asymptotic normality for the wavelet estimators and the convergence rates for the wavelet estimators of nonparametric components are investigated. A numerical example is given.

Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design

A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coeficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.

ESTIMATION THEORY OF A CLASS OF SEMIPARAMETRIC REGRESSION MODELS

Consider the semiparametric regression model Y=X’β+ g(T) + e, where (X,T) is R^p×[0,1]-valued random variables, βa p×1 vector of unknown parameter, g an unknown smoothfunction of T in [0,1], e the random error with mean 0 and variance σ~2】0, possiblyunknown. Assume that e and (X,T) are independent. In this paper, the estimatots ?, g_n~* and? of β,g and σ~2, respectively, based on the combination of nearest neighbor rule and leastsquare rule, are studied. The asymptotic normalities of ? and ? and tbe optimal con-vergence rate of g_n~* are obtained under suitable conditions.

ON B-SPLINE M-ESTIMATORS IN A SEMIPARAMETRIC REGRESSION MODEL

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区域差异导致经济块状发展的空间机理研究

本文运用空间计量经济学模型以及修正绝对β收敛回归模型,对中国2003-2007年省域经济发展的集聚性与差异性进行了研究,结果表明:中国31个省域之间存在着较强的空间集聚和空间依赖性,虽受到地域限制,但集聚辐射区域有逐步扩大的趋势;固定资产投入、人均实际工资以及城镇化率对于区域经济集聚的发展起到了稳健的推动作用,FDI对集聚区域发展的促进作用也越加显著,但是财政投入却在一定程度上遏制了块状经济的发展。另外,修正和传统收敛模型均显示,2003-2007年我国经济整体发展呈现明显的不收敛特性。

相依误差下异方差非参数回归模型的样条估计

一些经济金融等实际数据中含有非线性趋势、异方差和相依关系,固定设计和相依误差下的异方差非参数回归模型因其能够反映这些数据特征而有着重要的应用.样条方法是常用的非参数光滑方法之一.为了探究样条方法在这类模型中的可用性,本文在α-混合条件下,讨论了均值函数和方差函数的多项式样条估计的逐点相合性,得到了逐点收敛速度.此外,还对所讨论的方法进行了数值模拟,结果表明样条方法在这类模型的应用中是可行的.

空间依赖、空间异质与京津冀都市地区经济收敛

基于探索性空间数据分析技术(ESDA)划分出京津冀都市地区的中心区域和外围区域,并在传统经济收敛模型基础上,运用空间俱乐部收敛模型和局部空间回归模型对京津冀都市地区经济收敛情况进行研究。结果表明,首先,京津冀都市地区已形成了以北京、天津和唐山为核心的中心区域和以张家口市、保定市为核心的环绕京津的外围区域,京津冀都市地区整体上存在微弱的经济收敛。其次,京津冀都市地区中心地区由于经济发展水平较高,空间外溢效应较大,加之中心地区接受知识、技术扩散的能力较强,存在经济收敛,并且收敛速度较快,而外围区域则不存在经济收敛。再次,中心地区和外围地区内部存在经济收敛系数结构的不稳定性。