半参数回归模型的稳健补偿最小二乘估计

本文研究了一类半参数回归模型，利用稳健补偿最小二乘估计法，得到了稳健补偿最小二乘估计量，以及它们的影响函数及渐近方差一协方差，对结果的分析表明了该法优于补偿最小二乘法，而且具有稳定性．     

Central limit theorems for arrays of decimated linear processes

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time series, using wavelets.     

Generalized profile LSE in varying-coefficient partially linear models with measurement errors

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, ··· , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.     

A Semiparametric Model of Estimating Volatility of Diffusion Processes

This article provides a semiparametric model to estimate the diffusion coefficient of a stochastic differential equation from discretely observed data without assuming any functional form of the diffusion coefficient. It is shown that the model has the consistency such that estimated states of the diffusion coefficient converge to the true ones as the number of observations (N) goes to infinity and the sampling time interval (Δt) goes to zero while NΔt going to infinity.     

Transformation Kernel Density Estimation With Applications

One of the main objectives of this article is to derive efficient nonparametric estimators for an unknown density fX. It is well known that the ordinary kernel density estimator has, despite several good properties, some serious drawbacks. For example, it suffers from boundary bias and it also exhibits spurious bumps in the tails. We propose a semiparametric transformation kernel density estimator to overcome these defects. It is based on a new semiparametric transformation function that transforms data to normality. A generalized bandwidth adaptation procedure is also developed. It is found that the newly proposed semiparametric transformation kernel density estimator performs well for unimodal, low, and high kurtosis densities. Moreover, it detects and estimates densities with excessive curvature (e.g., modes and valleys) more effectively than existing procedures. In conclusion, practical examples based on real-life data are presented.     

Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure

A new class of power-transformed threshold ARCH models is proposed as a threshold-asymmetric generalization of the nonlinear ARCH considered by Higgins and Bera [Internat. Econom. Rev. 33 (1992) 137]. This class is rich enough to include diverse nonlinear and nonsymmetric ARCH models which have been spelled out in the literature. Geometric ergodicity of the model and existence of stationary moments are studied. The model facilitates discussing ARCH structures and hence large sample tests for ARCH structures are investigated via local asymptotic normality approach. Semiparametric tests are also discussed for the case when the error density is unknown.     

Nearest neighbor conditional estimation for Harris recurrent Markov chains

This paper is concerned with consistent nearest neighbor time series estimation for data generated by a Harris recurrent Markov chain on a general state space. It is shown that nearest neighbor estimation is consistent in this general time series context, using simple and weak conditions. The results proved here, establish consistency, in a unified manner, for a large variety of problems, e.g. autoregression function estimation, and, more generally, extremum estimators as well as sequential forecasting. Finally, under additional conditions, it is also shown that the estimators are asymptotically normal.