A note on finite population prediction under asymetric loss functions

The purpose of the present note is to derive optimal population total predictors relative to the Linex (Zellner, 1986) loss function under some well known superpopulation models. The risk function and Bayes risk are derived and compared with those of usual predictors. Minimax and and admissibility properties of some of the derived predictors are also investigated.     

On improvement in estimating population mean in stratified random sampling

Gupta and Shabbir 2 Gupta, S. and Shabbir, J. 2008. On improvement in estimating the population mean in simple random sampling. J. Appl. Stat., 35(5): 559–566. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] have suggested an alternative form of ratio-type estimators for estimating the population mean. In this paper, we obtained a corrected version for the mean square error (MSE) of the Gupta–Shabbir estimator, up to first order of approximation, and the optimum case is discussed. We expand this estimator to the stratified random sampling and propose general classes for combined and separate estimators. Also an empirical study is carried out to show the properties of the proposed estimators.     

A Monte Carlo comparison of some variance estimators of the Horvitz–Thompson estimator

At the design and estimation stage of a survey, large survey organization often uses auxiliary information. This article discusses various procedures for improving variance estimation of the Horvitz–Thompson estimator of a finite population total with the aid of auxiliary information. To study the design-based properties of the proposed variance estimators relative to the standard one, a small scale Monte Carlo study is performed.     

A new class of boundary kernels for distribution function estimation

In this note we introduce a new class of boundary kernels for distribution function estimation which shows itself to be especially performing when the classical kernel distribution function estimator suffers from severe boundary problems.     

A varying coefficient approach to estimating hedonic housing price functions and their quantiles

The varying coefficient (VC) model introduced by Hastie and Tibshirani [26 T. Hastie and R. Tibshirani, Varying-coefficient models, J. R. Statist. Soc. (Ser. B) 55 (1993), pp. 757–796.[Web of Science ®] , [Google Scholar]] is arguably one of the most remarkable recent developments in nonparametric regression theory. The VC model is an extension of the ordinary regression model where the coefficients are allowed to vary as smooth functions of an effect modifier possibly different from the regressors. The VC model reduces the modelling bias with its unique structure while also avoiding the ‘curse of dimensionality’ problem. While the VC model has been applied widely in a variety of disciplines, its application in economics has been minimal. The central goal of this paper is to apply VC modelling to the estimation of a hedonic house price function using data from Hong Kong, one of the world's most buoyant real estate markets. We demonstrate the advantages of the VC approach over traditional parametric and semi-parametric regressions in the face of a large number of regressors. We further combine VC modelling with quantile regression to examine the heterogeneity of the marginal effects of attributes across the distribution of housing prices.     

New estimators of distribution functions

ABSTRACT

This article considers the estimation of a distribution function F_X(x) based on a random sample X₁, X₂, …, X_n when the sample is suspected to come from a close-by distribution F₀(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F₀(x). As a by-product similar estimators are proposed for population quantiles.     

Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.     

Some calibration estimators for finite population mean in two-stage stratified random sampling

Abstract

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.     

A decision theoretic approach to ridits

Since its inception, ridit analyses has been in widespread use in epidemic-logic studies where the data are ordered but are not on an interval scale. However, no mathematical properties of ridits have been given. In this paper, we use a squared error loss function to show that, for a particular class of distribution functions, ridits form a best invariant estimate of the unknown distribution function. Under another class of distribution functions, we derive another estimate, m-ridits, of the distribution function. Data are used to compare these two scores with the scores obtained from the empirical distribution function and the original scores used on the data. The results indicate that, although these scores are numerically different, the same inferences can be drawn.     

A new estimator of finite population mean based on the dual use of the auxiliary information

When a sufficient correlation between the study variable and the auxiliary variable exists, the ranks of the auxiliary variable are also correlated with the study variable, and thus, these ranks can be used as an effective tool in increasing the precision of an estimator. In this paper, we propose a new improved estimator of the finite population mean that incorporates the supplementary information in forms of: (i) the auxiliary variable and (ii) ranks of the auxiliary variable. Mathematical expressions for the bias and the mean-squared error of the proposed estimator are derived under the first order of approximation. The theoretical and empirical studies reveal that the proposed estimator always performs better than the usual mean, ratio, product, exponential-ratio and -product, classical regression estimators, and Rao (1991 Rao, T.J. (1991). On certail methods of improving ration and regression estimators. Commun. Stat. Theory Methods 20(10):3325–3340.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Singh et al. (2009 Singh, R., Chauhan, P., Sawan, N., Smarandache, F. (2009). Improvement in estimating the population mean using exponential estimator in simple random sampling. Int. J. Stat. Econ. 3(A09):13–18. [Google Scholar]), Shabbir and Gupta (2010 Shabbir, J., Gupta, S. (2010). On estimating finite population mean in simple and stratified random sampling. Commun. Stat. Theory Methods 40(2):199–212.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Grover and Kaur (2011 Grover, L.K., Kaur, P. (2011). An improved estimator of the finite population mean in simple random sampling. Model Assisted Stat. Appl. 6(1):47–55. [Google Scholar], 2014) estimators.     

Some unbiased estimators versus mean per unit and ratio estimators in finite population sample surveys

We present some unbiased estimators at the population mean in a finite population sample surveys with simple random sampling design where information on an auxiliary variance x positively correlated with the main variate y is available. Exact variance and unbiased estimate of the variance are computed for any sample size. These estimators are compared for their precision with the mean per unit and the ratio estimators. Modifications of the estimators are suggested to make them more precise than the mean per unit estimator or the ratio estimator regardless of the value of the population correlation coefficient between the variates x and y. Asymptotic distribution of our estimators and confidnece intervals for the population mean are also obtained.     

A new approach to use multivariate auxiliary information in sample surveys

A new approach to form multivariate difference estimator is suggested which does not require the knowledge of unknown population parameters as such. It gives minimum variance among the class of multivariate difference estimators. The performance of this estimator with respect to Des Raj's (J. Amer. Statist. Assoc. 60 (1965), 270–277) multivariate difference estimator is illustrated. Using the information on two auxiliary variates, the robustness of Des Raj's estimator y_d is studied empirically. Two new estimators to estimate population mean/total are developed on the same lines as that of y_d. The performance of these estimators is studied for a wide variety of populations.     

The exact distribution and density functions of the stein-type estimator for normal variance

In this paper, we derive the exact distribution and density functions of the Stein-type estimator for the normal variance. It is shown by numerical evaluation that the density function of the Stein-type estimator is unimodal and concentrates around the mode more than that of the usual estimator.     

Nonparametric estimation of survival functions for incomplete observations when the life time distribution is proportionally related ot the censoring time distribution

Let X₁, X₂…,X_n be a random sample from [ILM0001] and let Y₁, …,Y_n be a random sample from [ILM0002]. Then instead of observing a complete sample X₁,…X_n, we can only observe the pairs Z_i. = min(X_i.,Y_i) and [ILM0003] In this paper, we consider estimation of survival function [ILM0004] when [ILM0005], where β is an unknown positive real number.

     

A study of ratio and product estimators under a super population model

In this paper ratio and product estimators are studied under a super population model considered by Durbin (1959. Biometrika) where a regression model of y (the characteristic variablel on x(the auxiliary variable) is assumed. The comparison of the ratio and the product estimators have been made in the literature (see Chaubey, Dwivedi and Singh (1984), Commun. Statist. - Theor. Meth.) When the auxiliary variable has a gamma distribution. In this paper similar analysis has been carried out when the auxiliary variable has an inverse Gaussian distribution.     

A new method for generating distributions with an application to exponential distribution

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in detail, namely one-parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment-generating function, mean residual lifetime, stochastic orders, order statistics, and expression of the entropies, are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non linear equations only. Further, we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes. Two datasets have been analyzed to show how the proposed models work in practice.     

A new approach to default priors and robust bayes methodology

Following the developments in DasGupta et al. (2000), the authors propose and explore a new method for constructing proper default priors and a method for selecting a Bayes estimate from a family. Their results are based on asymptotic expansions of certain marginal correlations. For ease of exposition, most results are presented for location families and squared error loss only. The default prior methodology amounts, ultimately, to the minimization of Fisher information, and hence, Bickel's prior works out as the default prior if the location parameter is bounded. As for the selected Bayes estimate, it corresponds to ‘Gaussian tilting’ of an initial reference prior.     

Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model data and then it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the IG goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. These tests are consistent against all alternatives. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by real data examples.     

Inference for linear and nonlinear stable error processes via estimating functions

This paper describes an estimating function approach for parameter estimation in linear and nonlinear times series models with infinite variance stable errors. Joint estimates of location and scale parameters are derived for classes of autoregressive (AR) models and random coefficient autoregressive (RCA) models with stable errors, as well as for AR models with stable autoregressive conditionally heteroscedastic (ARCH) errors. Fast, on-line, recursive parametric estimation for the location parameter based on estimating functions is discussed using simulation studies. A real financial time series is also discussed in some detail.     

Estimating parameters in a simple errors-in-variables model: a new approach base on finite sample distribution theory

This article presents a first direct application of finite sample distribution theory. The relevance of analytical finite sample research is exemplified in the framework of a simple linear errors-in-variables model (EV Model) with known or approximately known measurement error variance. Analytical results derived byRichardson/Wu (1970) are applied for constructing new approximately unbiased estimators for the slope coefficient in the EV model. The new estimators are compared with the biased least squares estimator and with asymptotic theory based corrected least squares estimators. Retaining responsibility for remaining errors the author is indebted to Prof. H. Schneewei\ and Prof. J. Gruber for helpful comments and discussions. Mrs. A. Brandtstater deserves special mention and thanks for performing the computations reported in section 4.