空间数据分析的发展

空间统计学是研究空间问题的一门学科,它是应用数学快速发展的一个分支。尽管传统的数据分析中有许多很好的方法,但却不能完全地套用于空间数据的分析。空间模型的估计不仅与各种回归形式的假设有关,而且还与空间相关、空间异质的特性有关。从空间模型及推断、适应性估计、非参数回归、空间不相关性检验几个方面研究了空间数据分析方法的发展以及未来的趋势。     

Functional Estimation of a Density Under a New Weak Dependence Condition

The purpose of this paper is to prove, through the analysis of the behaviour of a standard kernel density estimator, that the notion of weak dependence defined in a previous paper (cf. Doukhan & Louhichi, 1999) has sufficiently sharp properties to be used in various situations. More precisely we investigate the asymptotics of high order losses, asymptotic distributions and uniform almost sure behaviour of kernel density estimates. We prove that they are the same as for independent samples (with some restrictions for a.s. behaviours). Recall finally that this weak dependence condition extends on the previously defined ones such as mixing, association and it allows considerations of new classes such as weak shifts processes based on independent sequences as well as some non-mixing Markov processes.     

A BAYESIAN INTERPRETATION OF MULTIPLE POINT ESTIMATES

Consider a large number of econometric investigations using different estimation techniques and/or different subsets of all available data to estimate a fixed set of parameters. The resulting empirical distribution of point estimates can be shown - under suitable conditions - to coincide with a Bayesian posterior measure on the parameter space induced by a minimum information procedure. This Bayesian interpretation makes it easier to combine the results of various empirical exercises for statistical decision making. The collection of estimators may be generated by one investigator to ensure the satisfaction of our conditions, or they may be collected from published works, where behavioral assumptions need to be made regarding the dependence structure of econometric studies.     

DENSITY ESTIMATION FOR CLUSTERED DATA

The commonly used survey technique of clustering introduces dependence into sample data. Such data is frequently used in economic analysis, though the dependence induced by the sample structure of the data is often ignored. In this paper, the effect of clustering on the non-parametric, kernel estimate of the density, f(x), is examined. The window width commonly used for density estimation for the case of i.i.d. data is shown to no longer be optimal. A new optimal bandwidth using a higher-order kernel is proposed and is shown to give a smaller integrated mean squared error than two window widths which are widely used for the case of i.i.d. data. Several illustrations from simulation are provided.     

具有非负密度的粘性不可压缩流体运动的初边值问题的广义解的唯一性

本文讨论了一类具有非负密度的不可压缩流体运动的初边值问题,用积分估值法证明了这一模型广义解的唯一性.     

On the Bootstrap of the Maximum Score Estimator

This paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator. The theory developed also applies to other estimators within a cube‐root convergence class. For some single‐parameter estimators in this class, the results suggest a simple method for inference based upon the bootstrap.     

Statistical inference for start-up demonstration tests with rejection of units upon observing d failures

In this paper, we consider the statistical inference for the success probability in the case of start-up demonstration tests in which rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes are achieved for acceptance of the unit. Since the expected value of the stopping time is not a monotone function of the unknown parameter, the method of moments is not useful in this situation. Therefore, we discuss two estimation methods for the success probability: (1) the maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm and (2) Bayesian estimation with a beta prior. We examine the small-sample properties of the MLE and Bayesian estimator. Finally, we present an example to illustrate the method of inference discussed here.     

双重分层抽样中的校正估计

校正估计法已被大量运用于抽样调查中,它利用辅助信息构造的校正权重提高了对总体总值（或均值）的估计精度。本文提出了分层抽样中的校正组合比率估计量,并推广到分层双重抽样中。同时给出新估计量的近似方差表达式。最后利用计算机随机模拟验证较正估计量对估计精度的改进。     

基于平衡单水平轮换的连续性抽样估计方法研究

内容提要：针对现存的各种单水平轮换模式和估计方法,本文提出一套统一的平衡单水平轮换模式。在此轮换模式下,引入两类相关关系,运用线性无偏估计方法,并通过使不同类型估计量方差的加权总和最小的方法确定最优系数,从而得到最优线性无偏估计量,不仅能够减少甚至消除估计量偏差的影响,还能使得连续性调查的整体抽样误差最小,适合估计各种类型的估计量。     

Efficient estimation for the proportional hazards model with bivariate current status data

We consider efficient estimation of regression and association parameters jointly for bivariate current status data with the marginal proportional hazards model. Current status data occur in many fields including demographical studies and tumorigenicity experiments and several approaches have been proposed for regression analysis of univariate current status data. We discuss bivariate current status data and propose an efficient score estimation approach for the problem. In the approach, the copula model is used for joint survival function with the survival times assumed to follow the proportional hazards model marginally. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. A real life data application is provided for illustration.