In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity...In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.展开更多
By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation i...By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.展开更多
We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, i...We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.展开更多
This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conju...This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conjugate differential operator P_(r)(D)induced by■Also,the modulus of continuity of the r-th derivative,or r-th self-conjugate differential,does not exceed a given modulus of continuityω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.展开更多
We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed proces...We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.展开更多
The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of co...The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.展开更多
Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ ...Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.展开更多
In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has b...In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.展开更多
The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown f...The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.展开更多
The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the ...The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.展开更多
We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.
基金supported by the National Natural Science Foundation of China(12131015,12071422)。
文摘In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.
文摘By use of the approach of complex random signal processing, the asymptotic statistical properties of the least square estimates of 2-D exponential signals are studied. In doing so it is found that the representation is considerably more intuitive, and is analytically more tractable.
文摘We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.
基金supported by National Natural Science Foundation of China(11871006).
文摘This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conjugate differential operator P_(r)(D)induced by■Also,the modulus of continuity of the r-th derivative,or r-th self-conjugate differential,does not exceed a given modulus of continuityω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.
基金partially supported by the National Natural Science Foundation of China(11871244)the Fundamental Research Funds for the Central Universities,JLU。
文摘We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.
基金Supported by the National Natural Science Foundation of China(12101004)the Natural Science Research Project of Anhui Educational Committee(2023AH030021)the Research Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064)。
文摘The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.
文摘Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.
文摘In this paper, the optimal convergence rates of point estimators have been found under the irregular truncated distribution family, and corresponding Bahadurtype asymptotic efficiencies have been established. It has beed justified that commonly used estimators are all efficient in this sense.
基金Partially supported by the National Natural Science Foundation of China(10571136)
文摘The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
基金Supported by the Anhui Provincial Natural Science Foundation（11040606M04） Supported by the National Natural Science Foundation of China（10871001,10971097）
文摘The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.
基金Sponsored by the National Natural Science Foundation of China 10771163
文摘We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.
