Comparing three bootstrap methods for survey data

Various bootstrap methods for variance estimation and confidence intervals in complex survey data, where sampling is done without replacement, have been proposed in the literature. The oldest, and perhaps the most intuitively appealing, is the without-replacement bootstrap (BWO) method proposed by Gross (1980). Unfortunately, the BWO method is only applicable to very simple sampling situations. We first introduce extensions of the BWO method to more complex sampling designs. The performance of the BWO and two other bootstrap methods, the rescaling bootstrap (Rao and Wu 1988) and the mirror-match bootstrap (Sitter 1992), are then compared through a simulation study. Together these three methods encompass the various bootstrap proposals.     

A jackknife variance estimator for unequal probability sampling

Summary.  The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs. We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.     

Mixture Kalman filters

In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line 'filtering' task. We propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used non-linear systems and also serve to approximate many others. Compared with a few available filtering methods including Monte Carlo methods, the gain in efficiency that is provided by the mixture Kalman filter can be very substantial. Another contribution of the paper is the formulation of many non-linear systems into conditional or partial conditional linear form, to which the mixture Kalman filter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.     

Estimation of parameters and the mean life of a mixed failure time distribution

This paper deals with estimation of parameters and the mean life of a mixed failure time distribution that has a discrete probability mass at zero and an exponential distribution with mean O for positive values. A new sampling scheme similar to Jayade and Prasad (1990) is proposed for estimation of parameters. We derive expressions for biases and mean square errors (MSEs) of the maximum likelihood estimators (MLEs). We also obtain the uniformly minimum variance unbiased estimators (UMVUEs) of the parameters. We compare the estimator of O and mean life fj based on the proposed sampling scheme with the estimators obtained by using the sampling scheme of Jayade and Prasad (1990).     

A series of two-urn biased sampling problems

Much of the literature on matching problems in statistics has focused on single items chosen from independent, but fully overlapping sets. This paper considers a more general problem of sampling without replacement from partially overlapping sets and presents new theory on probability problems involving two urns and the selection of balls from these urns according to a biased without-replacement sampling scheme. The strength of the sampling bias is first considered as known, and then as unknown, with a discussion of how that strength may be assessed using observed data. Each scenario is illustrated with a numerical example, and the theory is applied to a gender bias problem in committee selection, and to a problem where competing retailers select products to place on promotion.     

Maximum Likelihood Estimation of Logistic Regression Parameters under Two-phase, Outcome-dependent Sampling

Outcome-dependent sampling increases the efficiency of studies of rare outcomes, examples being case—control studies in epidemiology and choice–based sampling in econometrics. Two-phase or double sampling is a standard technique for drawing efficient stratified samples. We develop maximum likelihood estimation of logistic regression coefficients for a hybrid two-phase, outcome–dependent sampling design. An algorithm is given for determining the estimates by repeated fitting of ordinary logistic regression models. Simulation results demonstrate the efficiency loss associated with alternative pseudolikelihood and weighted likelihood methods for certain data configurations. These results provide an efficient solution to the measurement error problem with validation sampling based on a discrete surrogate.     

Efficient Monte Carlo simulation via the generalized splitting method

We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives

The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.     

Inference in the Pareto distribution based on progressive Type II censoring with random removals

This study considers the estimation problem for the Pareto distribution based on progressive Type II censoring with random removals. The number of units removed at each failure time has a discrete uniform distribution. We are going to use the maximum likelihood method to obtain the estimator of parameter. The expectation and variance of the maximum likelihood estimator will be derived. The expected time required to complete such an experiment will be computed. Some numerical results of expected test times are carried out for this type of progressive censoring and other sampling schemes.     

In Memoriam: Martin Taitel,Francis E. McLntyre

A discrete uniform distribution is defined over the integers 1, 2, …, k. Following Tenenbein, who investigated the point estimation of k for a sample drawn without replacement, this paper considers a number of point estimators of k for sampling with replacement and presents conservative confidence sets for k for both methods of sampling.     

Hierarchical Bayes estimation in small area estimation using cross-sectional and time-series data

Bayesian methods have been extensively used in small area estimation. A linear model incorporating autocorrelated random effects and sampling errors was previously proposed in small area estimation using both cross-sectional and time-series data in the Bayesian paradigm. There are, however, many situations that we have time-related counts or proportions in small area estimation; for example, monthly dataset on the number of incidence in small areas. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data with incorporating cross-sectional and time-series data. The performance of the proposed approach is evaluated through several simulation studies and also by a real dataset.     

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.     

Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling

Sequential Monte Carlo methods (also known as particle filters and smoothers) are used for filtering and smoothing in general state-space models. These methods are based on importance sampling. In practice, it is often difficult to find a suitable proposal which allows effective importance sampling. This article develops an original particle filter and an original particle smoother which employ nonparametric importance sampling. The basic idea is to use a nonparametric estimate of the marginally optimal proposal. The proposed algorithms provide a better approximation of the filtering and smoothing distributions than standard methods. The methods’ advantage is most distinct in severely nonlinear situations. In contrast to most existing methods, they allow the use of quasi-Monte Carlo (QMC) sampling. In addition, they do not suffer from weight degeneration rendering a resampling step unnecessary. For the estimation of model parameters, an efficient on-line maximum-likelihood (ML) estimation technique is proposed which is also based on nonparametric approximations. All suggested algorithms have almost linear complexity for low-dimensional state-spaces. This is an advantage over standard smoothing and ML procedures. Particularly, all existing sequential Monte Carlo methods that incorporate QMC sampling have quadratic complexity. As an application, stochastic volatility estimation for high-frequency financial data is considered, which is of great importance in practice. The computer code is partly available as supplemental material.     

Small area estimation using unmatched sampling and linking models

The authors use a hierarchical Bayes approach to area level unmatched sampling and Unking models for small area estimation. Empirically they compare inferences under unmatched models with those obtained under the customary matched sampling and linking models. They apply the proposed method to Canadian census undercoverage estimation, developing a full hierarchical Bayes approach using Markov Chain Monte Carlo sampling methods. They show that the method can provide efficient model‐based estimates. They use posterior predictive distributions to assess model fit.     

Mass imputation for two-phase sampling

Two-phase sampling is a cost-effective method of data collection using outcome-dependent sampling for the second-phase sample. In order to make efficient use of auxiliary information and to improve domain estimation, mass imputation can be used in two-phase sampling. Rao and Sitter (1995) introduce mass imputation for two-phase sampling and its variance estimation under simple random sampling in both phases. In this paper, we extend the Rao–Sitter method to general sampling design. The proposed method is further extended to mass imputation for categorical data. A limited simulation study is performed to examine the performance of the proposed methods.     

The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carlo estimation for multilevel models with applications to discrete time survival models

Summary.  We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.     

基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

辅以排序集样本的分层抽样方法研究

分层抽样中,样本在各层中的不同获取方式会对估计量的精度和试验费用产生一定的影响,而已有的理论方法大多不能在提高精度的同时降低调查费用。为此,将排序抽样与分层抽样方法相结合,提出了辅以排序集样本的分层抽样方案,并得到了总体均值的估计量以及这一估计量的良好性质。这些结果表明,与单一的分层随机抽样相比,这种抽样设计的估计量具有更高的精度,同时也节约了各层抽样调查的费用。     

连续性抽样估计方法研究综述

根据国外的理论研究及应用的经验,预计连续性抽样估计方法在中国的应用前景非常广阔。因此,将连续性抽样估计方法作为研究对象,对国外已有的相关研究成果进行理论化、系统化的研究综述,并比较分析各类连续性抽样估计方法,归纳出存在的问题及未来研究的趋势,为后续的研究提供参考,同时为该方法顺利地应用到中国实际调查工作中奠定理论基础,从而进一步推动中国统计调查方法体系的改革与发展。