Adaptive composite estimation in small domains

Small area estimation techniques are used in sample surveys, where direct estimates for small domains are not reliable due to small sample sizes in the domains. We estimate the domain means by generalized linear compositions of the weighted sample means and the synthetic estimators that are obtained from the regression-synthetic model of fixed effects, based on the domain level auxiliary information. In the proposed method, the number of parameters of optimal compositions is reduced to a single unknown parameter, which is further evaluated by minimizing an empirical risk function. We apply various composite and related estimators to estimate proportions of the unemployed in a simulation study, based on the Lithuanian Labor Force Survey data. Conclusions on advantages and disadvantages of the proposed compositions are obtained from this empirical comparison.&nbsp

Design-based composite estimation of small proportions in small domains

Traditional direct estimation methods are inefficient for domains of a survey population with small sample sizes. To estimate the domain proportions, we combine the direct estimators and the regression-synthetic estimators based on domain-level auxiliary information. For the case of small true proportions, we propose the design-based linear combination that is a robust alternative to the empirical best linear unbiased predictor (EBLUP) based on the Fay–Herriot model. We imitate the Lithuanian Labor Force Survey, where we estimate the proportions of the unemployed and employed in municipalities. We show where the proposed design-based composition and estimator of its mean square error are competitive for EBLUP and its accuracy estimation

Estimation of parameters of finite population L-statistics

We consider the estimation of important parameters of a linear combination of order statistics (L-statistic) in a finite population, emphasizing the influence of auxiliary information on the estimation accuracy. Assuming that values of an auxiliary variable are available for all population units, we construct calibrated estimators for the variance of L-statistics and for the parameters, which define one-term Edgeworth expansions of distributions of L-statistics. The gain of the new estimators is demonstrated by the simulation study

An Edgeworth expansion for finite population L-statistics

In this paper, we consider the one-term Edgeworth expansion for finite population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity of the expansion which are expressed in terms of the weight function that defines the statistics and moment conditions.Comment: 14 pages. Minor revisions. Some explanatory comments and a numerical example were added. Lith. Math. J. (to appear

Baigtinių populiacijų L-statistikų savirankos, visrakčio ir Edžvorto aproksimacijos

In this paper we give exact bootstrap estimators for the parameters defining one-term Edgeworth expansion of distribution function of finite population L-statistic and compare these estimators with corresponding jackknife estimators. We also compare `````` true’ distribution of L-statistic with its normal approximation, Edgeworth expansion, empirical Edgeworth expansion and bootstrap approximation.Darbe tiriami baigtinių populiacijų L-statistikos Edžvorto skleidinio parametrų įvertiniai. Pateikiami tikslūs šių parametrų savirankos įvertiniai, kurie palyginami su atitinkamais visrakčio įvertiniais. Be to, „tikroji“ L-statistikos pasiskirstymo funkcija palyginama su jos normaliąja, Edžvorto, empirine Edžvorto ir savirankos aproksimacijomis

Approximations to distributions of linear combinations of order statistics in finite populations

Properties of linear combinations of order statistics (L-statistics), where samples are drawn without replacement, are considered in the thesis. The main object of the thesis is an improvement of the normal approximation to distributions of L-statistics by one-term Edgeworth expansions. An accuracy of these approximations is estimated using the Hoeffding decomposition of finite population symmetric statistics. In the first chapter of the thesis, explicit expressions of the first terms and remainder terms of the Hoeffding decomposition of L-statistics are obtained. The main applications of the decomposition are given in the second chapter: the optimal upper bound for variances of the sample minimum and maximum is obtained; sufficient conditions for the asymptotic normality of L-statistics are established; the one-term Edgeworth expansion for L-statistics is constructed and sufficient conditions for the validity of this approximation are obtained. In the third chapter, estimators of the variance and parameters that define the Edgeworth expansion of an L-statistic are constructed. In the fourth chapter, a one-term Edgeworth expansion for a Studentized L-statistic and empirical Edgeworth expansions are constructed and analyzed