Variance estimation of change in poverty rates and empirical likelihood inference in the presence of nuisance parameters under complex sampling designs

Abstract

This thesis includes three papers. The first paper demonstrates how to estimate variance of change in poverty rates under rotating complex sampling designs. Measuring variance of change enables practitioners to judge whether or not the observed changes over time are statistically significant. The main difficulty in estimation of variance of change under rotating designs arises in the estimation of correlations between cross sectional estimates. This paper addresses a multivariate linear regression approach that provides a valid correlation estimator. Furthermore, poverty rate is a complex statistic that depends on a poverty threshold, which is estimated from the survey data. The paper mainly contributes by taking into account the variability of the poverty threshold in variance estimation of change. The approach is applied to the Turkish eu-silc survey data. The second paper presents a design based inference in the presence of nuisance parameters by using an empirical likelihood approach. The main contribution of the paper is to develop an asymptotic theory to support the approach. The approach proposed can be used for testing and confidence intervals for finite population parameters such as (non)linear (generalised) regression parameters. For example, when comparing two nested models, the additional parameters are the parameters of interest, and the common parameters are the nuisance parameters. Sampling design and population level information are taken into account with the approach. Confidence intervals do not rely on resampling, linearisation, variance estimation, or design effects. The third paper shows how the empirical likelihood approach proposed in the second paper is applied to make inferences for regression coefficients when modelling hierarchical data collected from a two-stage sampling design where the first stage units may be selected with un-equal probabilities. Multilevel regressions are often employed in social sciences to analyse data with hierarchical structure. This paper considers fixed effect regression parameters that can be defined through `general estimating equations'. We use an `ultimate cluster approach' by treating the first stage sample units as the units of interest.

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Identifiers

ORCID for Yves Berger: orcid.org/0000-0002-9128-5384

ORCID for Li-Chun Zhang: orcid.org/0000-0002-3944-9484

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