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.     

Analysis of incomplete durations with application to contraceptive use

Models for analysing incomplete durations obtained from cross-sectional surveys are presented. The aim of the paper is to develop a framework for analysing the incomplete duration of episodes in progress at the time of the survey by formulating generalized linear models and fitting and assessing them by using standard statistical packages. The maximum quasi-likelihood method is used for model fitting. The choice of the distribution and the diagnostic procedures are discussed. Simulated data from two distributions (the Weibull and log-logistic distributions) are used to evaluate the methodology developed and to assess model misspecifications. A data set on the current use of the contraceptive pill from a cross-sectional survey in Egypt is analysed.     

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.     

Modified quasi-profile likelihoods from estimating functions

We discuss higher-order adjustments for a quasi-profile likelihood for a scalar parameter of interest, in order to alleviate some of the problems inherent to the presence of nuisance parameters, such as bias and inconsistency. Indeed, quasi-profile score functions for the parameter of interest have bias of order O(1)$\mathrm{O}(1)$, and such bias can lead to poor inference on the parameter of interest. The higher-order adjustments are obtained so that the adjusted quasi-profile score estimating function is unbiased and its variance is the negative expected derivative matrix of the adjusted profile estimating equation. The modified quasi-profile likelihood is then obtained as the integral of the adjusted profile estimating function. We discuss two methods for the computation of the modified quasi-profile likelihoods: a bootstrap simulation method and a first-order asymptotic expression, which can be simplified under an orthogonality assumption. Examples in the context of generalized linear models and of robust inference are provided, showing that the use of a modified quasi-profile likelihood ratio statistic may lead to coverage probabilities more accurate than those pertaining to first-order Wald-type confidence intervals.     

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.     

剩磁法估测三相交流异步电动机转速的分析

介绍一种用剩磁法估测三个交流异步电动机转速的新方法,并就这种方法的有关问题进行了初步分析。