Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non‐stationary Volatility

In this paper, we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to non‐stationary volatility. Extant estimators of the trend coefficient are analysed. We find that under heteroskedasticity, the Cochrane–Orcutt‐type estimator (with some initial condition) could be less efficient than Ordinary Least Squares (OLS) when the process is highly persistent, whereas it is asymptotically equivalent to OLS when the process is less persistent. An efficient non‐parametrically weighted Cochrane–Orcutt‐type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non‐stationary volatility of unknown form. The feasible estimator relies on non‐parametric estimation of the volatility function, and the asymptotic theory is provided. We use the data‐dependent smoothing bandwidth that can automatically adjust for the strength of non‐stationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of non‐stationary volatility. Finite‐sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators.     

Heteroscedastic Global Tests that the Regression Parameters for Two or More Independent Groups are Identical

Simulation results are reported on methods that allow both within group and between group heteroscedasticity when testing the hypothesis that independent groups have identical regression parameters. The methods are based on a combination of extant techniques, but their finite-sample properties have not been studied. Included are results on the impact of removing all leverage points or just bad leverage points. The method used to identify leverage points can be important and can improve control over the Type I error probability. Results are illustrated using data from the Well Elderly II study.     

Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Hill estimator of projections of functional data on principal components

Functional principal component scores are commonly used to reduce mathematically infinitely dimensional functional data to finite dimensional vectors. In certain applications, most notably in finance, these scores exhibit tail behaviour consistent with the assumption of regular variation. Knowledge of the index of the regular variation, α, is needed to apply methods of extreme value theory. The most commonly used method of the estimation of α is the Hill estimator. We derive conditions under which the Hill estimator computed from the sample scores is consistent for the tail index of the unobservable population scores.     

Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.     

Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

社会民主主义复兴的两种模式比较

20世纪90年代在社会民主主义复兴的过程中,英国和法国由于竞选方式、政策策略等一系列方面存在显著差别,被认为是社会民主主义复兴的两种典型模式,对英国道路与法国道路的相同之处和不同之处进行比较,说明二者存在共同性和差异性的原因。     

统一规制经济垄断与行政垄断的必要性与紧迫性

我国反垄断法所应规制的垄断一直是一个众说纷纭的问题。本文从经济垄断和行政垄断的共性的角度 ,提出了我国反垄断法应统一规制经济垄断和行政垄断。这不仅是建立社会主义市场经济的需要 ,也是我国入世后的必然要求     

一类带有分布参数系统的最佳控制

本文给出一类非均匀弦的横向振动的最佳控制，推广了P C Park的结果。这一结果同样适用于同类型振动问题。