arXiv subjects

J. N. K. Rao

Publications and source records attributed to J. N. K. Rao.

10 recordsLinked to original sources

arXiv2025

Pseudo Empirical Likelihood Inference for Non-Probability Survey Samples

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important research contributions to the field of survey sampling in general and the two topics in particular by Canadian survey statisticians. The authors then propose new inferential procedures on analyzing non-probability survey samples through the pseudo empirical likelihood approach. The proposed methods lead to asymptotically equivalent point estimators that have been discussed in the recent literature but possess more desirable features on confidence intervals such as range-respecting and data-driven orientation. Results from a simulation study demonstrate the superiority of the proposed methods in dealing with binary response variables.

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arXiv2025

Mean Squared Prediction Error Estimators of EBLUP of a Small Area Mean Under a Semi-Parametric Fay-Herriot Model

In this paper we derive a second-order unbiased (or nearly unbiased) mean squared prediction error (MSPE) estimator of the empirical best linear unbiased predictor (EBLUP) of a small area mean for a semi-parametric extension to the well-known Fay-Herriot model. Specifically, we derive our MSPE estimator essentially assuming certain moment conditions on both the sampling errors and random effects distributions. The normality-based Prasad-Rao MSPE estimator has a surprising robustness property in that it remains second-order unbiased under the non-normality of random effects when a simple Prasad-Rao method-of-moments estimator is used for the variance component and the sampling error distribution is normal. We show that the normality-based MSPE estimator is no longer second-order unbiased when the sampling error distribution has non-zero kurtosis or when the Fay-Herriot moment method is used to estimate the variance component, even when the sampling error distribution is normal. It is interesting to note that when the simple method-of moments estimator is used for the variance component, our proposed MSPE estimator does not require the estimation of kurtosis of the random effects. Results of a simulation study on the accuracy of the proposed MSPE estimator, under non-normality of both sampling and random effects distributions, are also presented.

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arXiv2023

Estimation of Poverty Measures for Small Areas Under a Two-Fold Nested Error Linear Regression Model: Comparison of Two Methods

Demand for reliable statistics at a local area (small area) level has greatly increased in recent years. Traditional area-specific estimators based on probability samples are not adequate because of small sample size or even zero sample size in a local area. As a result, methods based on models linking the areas are widely used. World Bank focused on estimating poverty measures, in particular poverty incidence and poverty gap called FGT measures, using a simulated census method, called ELL, based on a one-fold nested error model for a suitable transformation of the welfare variable. Modified ELL methods leading to significant gain in efficiency over ELL also have been proposed under the one-fold model. An advantage of ELL and modified ELL methods is that distributional assumptions on the random effects in the model are not needed. In this paper, we extend ELL and modified ELL to two-fold nested error models to estimate poverty indicators for areas (say a state) and subareas (say counties within a state). Our simulation results indicate that the modified ELL estimators lead to large efficiency gains over ELL at the area level and subarea level. Further, modified ELL method retaining both area and subarea estimated effects in the model (called MELL2) performs significantly better in terms of mean squared error (MSE) for sampled subareas than the modified ELL retaining only estimated area effect in the model (called MELL1).

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arXiv2021

Variable selection for longitudinal survey data

In this article we propose a new variable selection method for analyzing data collected from longitudinal sample surveys. The procedure is based on the survey-weighted quadratic inference function, which was recently introduced as an alternative to the survey-weighted generalized estimating function. Under the joint model-design framework, we introduce the penalized survey-weighted quadratic inference estimator and obtain sufficient conditions for the existence, weak consistency, sparsity and asymptotic normality. To illustrate the finite sample performance of the model selection procedure, we include a limited simulation study.

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arXiv2021

Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach

Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In particular, the actual type I error rates of tests of hypotheses using standard methods can be much bigger than the nominal significance level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests that involve the estimated covariance matrices of parameter estimates. In this paper, we present a unified approach to hypothesis testing that does not require computing the covariance matrices by constructing bootstrap approximations to weighted likelihood ratio statistics and weighted quasi-score statistics and establish the asymptotic validity of the proposed bootstrap tests. In addition, we also consider hypothesis testing from categorical data and present a bootstrap procedure for testing simple goodness of fit and independence in a two-way table. In the simulation studies, the type I error rates of the proposed approach are much closer to their nominal significance level compared with the naive likelihood-ratio test and quasi-score test. An application to data from an educational survey under a logistic regression model is also presented.

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arXiv2020

Empirical Likelihood Inference With Public-Use Survey Data

Public-use survey data are an important source of information for researchers in social science and health studies to build statistical models and make inferences on the target finite population. This paper presents two general inferential tools through the pseudo empirical likelihood and the sample empirical likelihood methods. Theoretical results on point estimation and linear or nonlinear hypothesis tests involving parameters defined through estimating equations are established, and practical issues with the implementation of the proposed methods are discussed. Results from simulation studies and an application to the 2016 General Social Survey dataset of Statistics Canada show that the proposed methods work well under different scenarios. The inferential procedures and theoretical results presented in the paper make the empirical likelihood a practically useful tool for users of complex survey data.

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arXiv2014

Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach

Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to 'borrow strength" from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.

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arXiv2011

Rejoinder

Rejoinder of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao [arXiv:1108.2356]

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arXiv2011

Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal

According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are advanced for the wide use of this design-based approach, particularly by federal agencies and other survey organizations conducting complex large scale surveys on topics related to public policy. Impact of Bayesian methods in survey sampling is also discussed in two different directions: nonparametric calibrated Bayesian inferences from large samples and hierarchical Bayes methods for small area estimation based on parametric models.

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arXiv2004

Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

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