Using information from demographic analysis in post-enumeration survey estimation

"Population estimates from the 1990 Post-Enumeration Survey (PES), used to measure decennial census undercount, were obtained from dual system estimates (DSE's) that assumed independence within strata defined by age-race-sex-geography and other variables. We make this independence assumption for females, but develop methods to avoid the independence assumption for males within strata by using national level sex ratios from demographic analysis (DA).... We consider several...alternative DSE's, and use DA results for 1990 to apply them to data from the 1990 U.S. census and PES."     

中国农业普查事后质量抽查

一、ＰＥＳ数据分析模型由于抽查不只是对普查的重复 ,而是针对已进行的调查来收集“真实值”的一种方法。在中国 ,ＰＥＳ的入户访问是按与普查相同的环境来进行的 ,目的是要得到尽可能接近真实的调查结果。从ＰＥＳ得到的数据要与普查数据相比较。对两次调查的回答逐一比较 ,会得到如下的结果 :①普查和抽查回答一致 ;②两次调查的回答不一致 :回答的差别越大 ,普查估计的可靠性就越低。ＰＥＳ是为了检查和评估普查的数据质量。对ＰＥＳ回答误差的研究表明 ,回答误差也影响了ＰＥＳ数据。下面 ,我们将对两次调查同等对待。估计可靠性的指标…     

A three-sample multiple-recapture approach to census population estimation with heterogeneous catchability

"A central assumption in the standard capture-recapture approach to the estimation of the size of a closed population is the homogeneity of the 'capture' probabilities. In this article we develop an approach that allows for varying susceptibility to capture through individual parameters using a variant of the Rasch model from psychological measurement situations. Our approach requires an additional recapture. In the context of census undercount estimation, this requirement amounts to the use of a second independent sample or alternative data source to be matched with census and Post-Enumeration Survey (PES) data.... We illustrate [our] models and their estimation using data from a 1988 dress-rehearsal study for the 1990 census conducted by the U.S. Bureau of the Census, which explored the use of administrative data as a supplement to the PES. The article includes a discussion of extensions and related models."     

Total error in PES estimates of population

"We describe a methodology for estimating the accuracy of dual systems estimates (DSE's) of population, census estimates of population, and estimates of undercount in the census. The DSE's are based on the census and a post-enumeration survey (PES). We apply the methodology to the 1988 dress rehearsal census of St. Louis and east-central Missouri and we discuss its applicability to the 1990 [U.S.] census and PES. The methodology is based on decompositions of the total (or net) error into components, such as sampling error, matching error, and other nonsampling errors. Limited information about the accuracy of certain components of error, notably failure of assumptions in the 'capture-recapture' model, but others as well, lead us to offer tentative estimates of the errors of the census, DSE, and undercount estimates for 1988. Improved estimates are anticipated for 1990." Comments are included by Eugene P. Ericksen and Joseph B. Kadane (pp. 855-7) and Kenneth W. Wachter and Terence P. Speed (pp. 858-61), as well as a rejoinder by Mulry and Spencer (pp. 861-3).     

Hierarchical logistic regression models for imputation of unresolved enumeration status in undercount estimation

"In this article we describe a logistic regression modeling approach for nonresponse in the [U.S.] Post-Enumeration Survey (PES) that has desirable theoretical properties and that has performed well in practice.... In the 1990 PES, interviews were not obtained from approximately 1.2% of households in the sample, and approximately 2.1% of the individuals in interviewed households were considered unresolved after follow-up....The missing binary enumeration statuses for these unresolved cases were replaced with probabilities estimated under a statistical model that incorporated covariate information observed for these cases. This article describes an approach to modeling missing binary outcomes when there are a large number of covariates."     

Assessing between-block heterogeneity within the post-strata of the 1990 Post-Enumeration Survey

"The 1990 [U.S.] Post-Enumeration Survey (PES) stratified the population into 1,392 subpopulations called post-strata based on location, race, tenure, sex and age, in the hope that these subpopulations were homogeneous in relation to factors affecting the Census coverage....With block-level data from the PES for sites around Detroit and Texas, we are able to examine empirically the extent to which this hope was realized. Using various measures, we find that between-block variation in erroneous enumeration and gross omission rates is about the same magnitude as, and largely in addition to, the corresponding between-post-stratum variation." Comments by Joseph L. Schafer and Donald Ylvisaker and a rejoinder by the authors are included (pp. 1,125-9).     

Accuracy of the 1990 census and undercount adjustments

"In July 1991 the [U.S.] Census Bureau recommended to its parent agency, the Department of Commerce, that the 1990 census be adjusted for undercount. The Secretary of Commerce decided not to adjust, however. Those decisions relied at least partly on the Census Bureau's analyses of the accuracy of the census and of the proposed undercount adjustments based on the Post-Enumeration Survey (PES).... This article describes the total error analysis and loss function analysis of the Census Bureau. In its decision not to adjust the census, the Department of Commerce cited different criteria than aggregate loss functions. Those criteria are identified and discussed."     

Combining census,dual-system,and evaluation study data to estimate population shares

"The 1990 [U.S.] census and Post-Enumeration Survey produced census and dual system estimates (DSE) of population by domain, together with an estimated sampling covariance matrix of the DSE. Estimates of the bias of the DSE were derived from various PES evaluation programs. Of the three sources, the unadjusted census is the least variable but is believed to be the most biased, the DSE is less biased but more variable, and the bias estimates may be regarded as unbiased but are the most variable. This article addresses methods for combining the census, the DSE, and bias estimates obtained from the evaluation programs to produce accurate estimates of population shares, as measured by weighted squared- or absolute-error loss functions applied to estimated population shares of domains."     

A log-linear regression model for the odd Weibull distribution with censored data

We introduce the log-odd Weibull regression model based on the odd Weibull distribution (Cooray, 2006). We derive some mathematical properties of the log-transformed distribution. The new regression model represents a parametric family of models that includes as sub-models some widely known regression models that can be applied to censored survival data. We employ a frequentist analysis and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to assess global influence. Further, for different parameter settings, sample sizes and censoring percentages, some simulations are performed. In addition, the empirical distribution of some modified residuals are given and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to check the model assumptions. The extended regression model is very useful for the analysis of real data.     

Robust inference by influence functions

We first review briefly some basic approaches to robust inference and discuss the role and the place of some key concepts (influence function, breakdown point, robustness versus efficiency, etc.). We then discuss in some detail recent results on robust testing in general multivariate parametric models. Recent applications include inference in logistic regression and testing for non-nested hypotheses.     

Strong laws of large numbers for sub-linear expectation without independence

In this paper, we investigate some strong laws of large numbers for sub-linear expectation without independence which generalize the classical ones. We give some strong laws of large numbers for sub-linear expectation on some moment conditions with respect to the partial sum and some conditions similar to Petrov’s. We can reduce the conclusion to a simple form when the the sequence of random variables is i.i.d. We also show a strong law of large numbers for sub-linear expectation with assumptions of quasi-surely.     

Failure time regression with continuous covariates measured with error

We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on-going epidemiologic study.     

Consistent and rate-optimal density estimation from heteroscedastic data groups

We consider the problem of estimating a density function based on aggregated data where the data group sizes may differ from each other. The reconstruction of the target density can be regarded as a nonlinear statistical inverse problem. We introduce some estimation procedures which are capable to use the observations from all groups by some nonstandard deconvolution techniques. General consistency and rate-optimality under common smoothness constraints are developed. We give some numerical simulations and a data-driven bandwidth selector.     

Privacy protection measures for randomized response surveys on stigmatizing continuous variables

We consider the situation where sample surveys are to be undertaken on sensitive or stigmatizing issues. For such surveys, direct questioning methods usually lead to non-compliance or incorrect responses and so, the randomized response technique, where the responses are collected through some randomization device, is found to be useful. A majority of the literature on these techniques focus on dichotomous sensitive variables, while some techniques are also available for continuous sensitive variables. In this article, we focus on the extent of privacy protection available in sample surveys to respondents for continuous response variables. We also propose two measures of privacy protection. We demonstrate that the parameters of our randomization scheme can be so chosen as to achieve a pre-assigned level of privacy protection while at the same time yielding efficient estimates. We also show some numerical comparisons.     

On Multi-Treatment Adaptive Allocation Design for Dichotomous Response

The use of ridit, as a probability score, is a very common practice to compare discrete random variables in discrete data analysis. In the present work we formulate ridit reliability functionals for some comparison of K independent binary random variables. We use such functionals to provide a generalized response-adaptive design (GRAD) on K(≥ +2) treatment-arms for dichotomous response variables. We exhibit some properties of the proposed design and compare it with some of the existing competitors by computing its various performance measures. We also provide a discussion towards a possible modification of the GRAD in the presence of covariates.     

Semi-Sequential One-Shot Monitoring of Small Disorders With Controlled Type I Error Rate

We propose a simple two-stage monitoring rule for detecting small disorders in a two-sample location problem. The proposed rule is based on ranks and hence is nonparametric in nature. In the first stage, we use a sequential monitoring scheme to decide the necessity of employing a location test at some point of time. If there is urgency, we simply use a two-sample Wilcoxon rank sum test in the second stage. This leads to a semi sequential one-shot monitoring procedure. We study some asymptotic performance of the proposed rule. We also present some numerical findings obtained through Monte Carlo studies. The proposed rule meets the challenge of controlling type I error rate in sequential monitoring of an incoming series of observations.     

Log-linear models for mutations in the HIV genome

We discuss a general application of categorical data analysis to mutations along the HIV genome. We consider a multidimensional table for several positions at the same time. Due to the complexity of the multidimensional table, we may collapse it by pooling some categories. However, the association between the remaining variables may not be the same as before collapsing. We discuss the collapsibility of tables and the change in the meaning of parameters after collapsing categories. We also address this problem with a log-linear model. We present a parameterization with the consensus output as the reference cell as is appropriate to explain genomic mutations in HIV. We also consider five null hypotheses and some classical methods to address them. We illustrate methods for six positions along the HIV genome, through consideration of all triples of positions.     

Invariance properties of some classical tests for exponentiality

We examine some classical tests for the exponentiality of independent, identically distributed data. We show that a large number of these tests have the same distribution if the data follow certain multivariate Liouville distributions. These results highlight the role that the assumption of independence plays in the behavior of the classical test statistics. We use these results to derive some characterizations of the exponential distributions among the Liouville distributions.     

Extension of some large deviation results for posterior distributions

We consider a family of statistical models with positive unknown parameter (which includes some well-known models for censored exponential data) and some statistical models for samples from stationary Gaussian processes. We prove large deviation results for posterior distributions and, in some cases, also for maximum likelihood estimators.     

A new variability order based on tail-heaviness

In this paper, we introduce a new variability order that can be interpreted in terms of tail-heaviness which we will call the tail dispersive order. We provide the new definition, its interpretation and properties and the main characterization. We also study the relationship with other classical variability orders. Finally, we study the tail dispersive order in some classical parametric families and provide some applications in insurance and finance. We conclude with a numerical example applied to log returns distributions.