Calibrated linear unbiased estimators in finite population sampling

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].     

Logistic regression analysis of randomized response data with missing covariates

Randomized response is an interview technique designed to eliminate response bias when sensitive questions are asked. In this paper, we present a logistic regression model on randomized response data when the covariates on some subjects are missing at random. In particular, we propose Horvitz and Thompson (1952)-type weighted estimators by using different estimates of the selection probabilities. We present large sample theory for the proposed estimators and show that they are more efficient than the estimator using the true selection probabilities. Simulation results support theoretical analysis. We also illustrate the approach using data from a survey of cable TV.     

The exact density of nonparametric regression estimators: fixed design case

This paper studies the exact density of a general nonparametric regression estimator when the errors are non-normal. The fixed design case is considered. The density function is derived by an application of the technique of Davis (1976)     

Incorporating historical controls using a random-effects model with a normal prior

Employing a variance stabilization transformation, a random-effects model with a normal prior is proposed for incorporating historical controls in the estimation of dose-response relationships. The advantages and disadvantages of maximum likelihood and empirical Bayes estimators are discussed. A two-stage method is introduced for the prudent use of historical controls.     

ON ESTIMATION FOLLOWING SELECTION FROM NONREGULAR DISTRIBUTIONS

Independent random samples are drawn from k (≥ 2) populations, having probability density functions belonging to a general truncation parameter family. The populations associated with the smallest and the largest truncation parameters are called the lower extreme population (LEP) and the upper extreme population (UEP), respectively. For the goal of selecting the LEP (UEP), we consider the natural selection rule, which selects the population corresponding to the smallest (largest) of k maximum likelihood estimates as the LEP (UEP), and study the problem of estimating the truncation parameter of the selected population. We unify some of the existing results, available in the literature for specific distributions, by deriving the uniformly minimum variance unbiased estimator (UMVUE) for the truncation parameter of the selected population. The conditional unbiasedness of the UMVUE is also checked. The cases of the left and the right truncation parameter families are dealt with separately. Finally, we consider an application to the Pareto probability model, where the performances of the UMVUE and three other natural estimators are compared with each other, under the mean squared error criterion.     

Small area estimation of poverty indicators

The authors propose to estimate nonlinear small area population parameters by using the empirical Bayes (best) method, based on a nested error model. They focus on poverty indicators as particular nonlinear parameters of interest, but the proposed methodology is applicable to general nonlinear parameters. They use a parametric bootstrap method to estimate the mean squared error of the empirical best estimators. They also study small sample properties of these estimators by model‐based and design‐based simulation studies. Results show large reductions in mean squared error relative to direct area‐specific estimators and other estimators obtained by “simulated” censuses. The authors also apply the proposed method to estimate poverty incidences and poverty gaps in Spanish provinces by gender with mean squared errors estimated by the mentioned parametric bootstrap method. For the Spanish data, results show a significant reduction in coefficient of variation of the proposed empirical best estimators over direct estimators for practically all domains. The Canadian Journal of Statistics 38: 369–385; 2010 © 2010 Statistical Society of Canada     

Precedence-type test based on Kaplan–Meier estimator of cumulative distribution function

In this paper, we introduce a precedence-type test based on Kaplan–Meier estimator of cumulative distribution function (CDF) for testing the hypothesis that two distribution functions are equal against a stochastically ordered hypothesis. This test is an alternative to the precedence life-test proposed first by Nelson (1963). After deriving the null distribution of the test statistic, we present its exact power function under the Lehmann alternative, and compare the exact power as well as simulated power (under location-shift) of the proposed test with other precedence-type tests. Next, we extend this test to the case of progressively Type-II censored data. Critical values for some combination of sample sizes and progressive censoring schemes are presented. We then examine the power properties of this test procedure and compare them to those of the weighted precedence and weighted maximal precedence tests under a location-shift alternative by means of Monte Carlo simulations. Finally, we present two examples to illustrate all the test procedures discussed here, and then make some concluding remarks.     

Double-sampling regression-cum-exponential estimator of the mean of a sensitive variable

ABSTRACT

A flexible scrambled response model using a randomization device for quantitative sensitive data is used to evaluate the protection of respondents’ privacy. A double-sampling regression-cum-exponential estimator is used to estimate the mean of a sensitive variable using the mean of a nonsensitive auxiliary variable under scrambled response. The expected bias, the expected mean square error, and the minimum mean square error of this exponential-type estimator are expressed. Simulations and empirical results show that the proposed estimator under scrambled response model has a lower mean square error and a lower bias than the ratio and the exponential estimators.     

The general expressions for the moments of lawless and wang's ordinary ridge regression estimator

In this paper, we derive the exact general expressions for the moments of an ordinary ridge regression (ORR) estimator for individual regression coefficients in a different way from Firinguetti (1987). Using the derived expressions, we evaluate numerically the first four moments of the ORR estimator, and examine its bias, mean square error, skewness and kurtosis. Further, Monte Carlo experiments are carried out in order to examine the shape of the density function of the ORR estimator.     

Estimation of reliability under ordered restriction on the parameters

This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability.