Bootstrap estimation of actual significance levels for tests based on estimated nuisance parameters

Often for a non-regular parametric hypothesis, a tractable test statistic involves a nuisance parameter. A common practice is to replace the unknown nuisance parameter by its estimator. The validality of such a replacement can only be justified for an infinite sample in the sense that under appropriate conditions the asymptotic distribution of the statistic under the null hypothesis is unchanged when the nuisance parameter is replaced by its estimator (Crowder M.J. 1990. Biometrika 77: 499–506). We propose a bootstrap method to calibrate the error incurred in the significance level, for finite samples, due to the replacement. Further, we have proved that the bootstrap method provides a more accurate estimator for the unknown actual significance level than the nominal level. Simulations demonstrate the proposed methodology.     

Global optimization of the generalized cross-validation criterion

Generalized cross-validation is a method for choosing the smoothing parameter in smoothing splines and related regularization problems. This method requires the global minimization of the generalized cross-validation function. In this paper an algorithm based on interval analysis is presented to find the globally optimal value for the smoothing parameter, and a numerical example illustrates the performance of the algorithm.     

Empirical likelihood based diagnostics for heteroscedasticity in partially linear errors-in-variables models

A standard assumption in regression analysis is homogeneity of the error variance. Violation of this assumption can have adverse consequences for the efficiency of estimators. In this paper, we propose an empirical likelihood based diagnostic technique for heteroscedasticity in the partially linear errors-in-variables models. Under mild conditions, a nonparametric version of Wilk's theorem is derived. Simulation results reveal that our test performs well in both size and power.     

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171–1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605–610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897–916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples.     

Sequential estimation of a location parameter from delayed observations

The problem of sequentially estimating a location parameter is considered in the special case when the data arrive at random times. Certain classes of sequential estimation procedures are derived under a location invariant loss function and with the observation cost determined by a function of the moment of stopping and the number of observations up to this moment.     

线性GMDH参数模型的无偏估计研究

 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论：一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。     

非傍轴截断余弦高斯光束的光束传输因子

基于功率密度的二阶矩方法,对非傍轴截断余弦高斯光束的远场发散角和光束传输因子进行了系统研究.计算结果表明,非傍轴截断余弦高斯光束的光束传输因子不仅与截断参数δ、偏心参数α有关,而且还与初始束腰宽度和波长之比w0/λ有关.当截断参数δ→0时,远场发散角θ0趋于渐近值θ0max=63.4350.     

A proportional-hazards model for survival analysis and long-term survivors modeling: application to amyotrophic lateral sclerosis data

The majority of survival data are affected by explanatory variables. We develop a new regression model for survival data analysis. As an alternative to standard mixture models, another model is proposed to describe the eventual presence of a surviving fraction. The proposed models are based on the Marshall–Olkin extended generalized Gompertz distribution. A maximum-likelihood inference is presented in the presence of covariates and a censorship phenomenon. Explanatory variables are incorporated into the model through proportional-hazards to evaluate the effect of risk factors on overall survival under different assumptions. Parametric, semi-parametric, and non-parametric methods are applied to survival analysis of patients treated for amyotrophic lateral sclerosis. Interesting results about riluzole use and other treatment effects on patients'' survival have been obtained.     

积极财政政策的全要素生产率增长效应

利用时变参数模型和面板数据模型,可以对积极财政政策的全要素生产率增长效应进行分析。分析表明,1998年以来我国实施的积极财政政策对全国经济全要素生产率增长、省份经济全要素生产率增长和技术进步具有较强的促进作用,但对省份经济效率提高却具有明显的抑制作用。总体上说,积极财政政策对我国经济增长质量的提高起到了重要的促进作用,但在具体实施的过程中,还存在着诸如支出结构不尽合理、过分强调数量而忽视使用效率等不足之处。