Analysis of short-term systematic measurement error variance for the difference of paired data without repetition of measurement

The variance of short-term systematic measurement errors for the difference of paired data is estimated. The difference of paired data is determined by subtracting the measurement results of two methods, which measure the same item only once without measurement repetition. The unbiased estimators for short-term systematic measurement error variances based on the one-way random effects model are not fit for practical purpose because they can be negative. The estimators, which are derived for balanced data as well as for unbalanced data, are always positive but biased. The basis of these positive estimators is the one-way random effects model. The biases, variances, and the mean squared errors of the positive estimators are derived as well as their estimators. The positive estimators are fit for practical purpose.     

Some New Estimators for Small-Area Means With Application to the Assessment of Farmland Values

Regression models that account for main state effects and nested county effects are considered for the assessment of farmland values. Empirical predictors obtained by replacing the unknown variances in the formulas of the optimal predictors by maximum likelihood estimates are presented. The computations are carried out by simple iterations between two SAS procedures. Estimators for the prediction variances are derived, and a modification to secure the robustness of the predictors is proposed. The procedure is applied to data on nonirrigated cropland in the Corn Belt states and is shown to yield predictors with considerably lower prediction mean squared errors than the survey estimators and other regression-type estimators.     

A comparison of estimators of the precision of two instruments

Three different estimators of the variance in errors of measurement, or the “imprecisions” of instruments, have been proposed (Hahn and Nelson, 1970; Maxwell, 1974; Hanumara: 1975) for the case where two measurements by one instrument and one measurement by a second instrument are available for each item. The estimators are compared by studying the probabilities of negative values, the biases, the variances, and the mean square errors. Based on these results, Hahn and Nelson's estimators for the variances in errors of measurement are recommended. Simultaneous confidence intervals of the imprecisions of instruments are also given.     

Estimation for the semipareto processes

This paper proposes different estimators for the parameters of SemiPareto and Pareto autoregressive minification processes The asymptotic properties of the estimators are established by showing that the SemiPareto process is α-mixing. Asymptotic variances of different moment and maximum likelihood estimators are compared.     

Inferences for generalized exponential distribution based on record statistics

In this paper we consider three parameter generalized exponential distribution. Exact expressions for single and product moments of record statistics are derived. These expressions are written in terms of Riemann zeta and polygamma functions. Recurrence relations for single and product moments of record statistics are also obtained. These relations can be used to obtain the higher order moments from those of the lower order. The means, variances and covariances of the record statistics are computed for various values of the shape parameter and for some record statistics. These values are used to compute the coefficients of the best linear unbiased estimators of the location and scale parameters. The variances of these estimators are also presented. The predictors of the future record statistics are also discussed.     

Estimating Quantiles of Normal Populations with a Common Mean

Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known estimators of a common mean. Inadmissibility results are proved for estimators which are equivariant under affine and location groups of transformations. Risk values of various estimators of a quantile are compared numerically using a detailed simulation study.     

Cramér-Rao lower bounds for estimators based on censored data

The Cramér-Rao lower bounds for the variances of unbiased estimators based on censored data are given. Useful techniques of evaluation are then derived for these lower bounds. Examples are given to illustrate these techniques. Small-sample comparisons are made between the resulting lower bounds, the variances of the best linear unbiased estimators, and the variances of unbiased esti-mators which are based on the maximum likelihood estimators.     

Properties of maximum likelihood estimators of variance components in the one-way classification,balanced data

We studied properties of maximum likelihood estimators (MLEs) of the variance components obtained from balanced data of the one-way classification. Exact and asymptotic expected values and variances of these MLEs were derived under the usual normality assumptions. Numerical studies illustrate these expected values and variances, and also illustrate the probability of obtaining a negative solution to the maximum likelihood (ML) equation for the between-class variance component. Simulations were used to study the robustness of the ML estimators under non-normal distributions.     

Smoothing spline estimation in varying-coefficient models

Summary.  Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian 'confidence intervals' are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small simulation study and the analysis of a real data set.     

Estimation of two order restricted normal means with unknown and possibly unequal variances

Estimation of each of and linear functions of two order restricted normal means is considered when variances are unknown and possibly unequal. We replace unknown variances with sample variances and construct isotonic regression estimators, which we call in our paper the plug-in estimators, to estimate ordered normal means. Under squared error loss, a necessary and sufficient condition is given for the plug-in estimators to improve upon the unrestricted maximum likelihood estimators uniformly. As for the estimation of linear functions of ordered normal means, we also show that when variances are known, the restricted maximum likelihood estimator always improves upon the unrestricted maximum likelihood estimator uniformly, but when variances are unknown, the plug-in estimator does not always improve upon the unrestricted maximum likelihood estimator uniformly.     

On unbiased estimation of gini index and yntema-pietra index of lognormal distribution and their variances

Here we derive the uniformly minimum variance unbiased (best) estimator and a strongly consistent, asymptotically normal, unbiased estimator of each of Gini index and Yntema-Pietra index of lognormal distribution . These estimators are in terms of generalized hypergeometric functions ₁F₂. Further, the variances of these estimators and the best estimators of variances of best estimators are found out. They are in terms of Kempé de Fériet's hypergeometric functions.     

Empirical Bayes confidence intervals shrinking both means and variances

Summary.  We construct empirical Bayes intervals for a large number p of means. The existing intervals in the literature assume that variances     are either equal or unequal but known. When the variances are unequal and unknown, the suggestion is typically to replace them by unbiased estimators     . However, when p is large, there would be advantage in 'borrowing strength' from each other. We derive double-shrinkage intervals for means on the basis of our empirical Bayes estimators that shrink both the means and the variances. Analytical and simulation studies and application to a real data set show that, compared with the t -intervals, our intervals have higher coverage probabilities while yielding shorter lengths on average. The double-shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone. Also, the intervals are explicitly defined and can be computed immediately.     

An extension of Franklin's randomized response technique for multi-proportions

ABSTRACT

In this article, we introduce six estimators, three based on row averages and the remaining three on column averages of population proportions for trichotomous population when randomized response sampling with a normal randomizing distribution is used. The estimators have been obtained using the method of moments. All the proposed estimators are shown to be unbiased and their variances have been worked out. The percent relative efficiencies of the column total based estimators with respect to row total based estimators are investigated through empirical study.     

Letter to the editor comments on Groparu-Cojocaru and Doray (2013)

Although estimating the five parameters of an unknown Generalized Normal Laplace (GNL) density by minimizing the distance between the empirical and true characteristic functions seems appealing, the approach cannot be advocated in practice. This conclusion is based on extensive numerical simulations in which a fast minimization procedure delivers deceiving estimators with values that are quite far away from the truth. These findings can be predicted by the very large values obtained for the true asymptotic variances of the estimators of the five parameters of the true GNL density.     

MODEL-BASED VARIANCE ESTIMATION IN SURVEYS WITH STRATIFIED CLUSTERED DESIGN

A model-based method for estimating the sampling variances of estimators of (sub-)population means, proportions, quantiles, and regression parameters in surveys with stratified clustered design is described and applied to a survey of US secondary education. The method is compared with the jackknife by a simulation study. The model-based estimators of the sampling variances have much smaller mean squared errors than their jackknife counterparts. In addition, they can be improved by incorporating information about the unknown parameters (variances) from external sources. A regression-based smoothing method for estimating the sampling variances of the estimators for a large number of subpopulation means is proposed. Such smoothing may be invaluable when subpopulations are represented in the sample by only few subjects.     

Bayesian Estimators for Small Area Models Shrinking Both Means and Variances

For small area estimation of area‐level data, the Fay–Herriot model is extensively used as a model‐based method. In the Fay–Herriot model, it is conventionally assumed that the sampling variances are known, whereas estimators of sampling variances are used in practice. Thus, the settings of knowing sampling variances are unrealistic, and several methods are proposed to overcome this problem. In this paper, we assume the situation where the direct estimators of the sampling variances are available as well as the sample means. Using this information, we propose a Bayesian yet objective method producing shrinkage estimation of both means and variances in the Fay–Herriot model. We consider the hierarchical structure for the sampling variances, and we set uniform prior on model parameters to keep objectivity of the proposed model. For validity of the posterior inference, we show under mild conditions that the posterior distribution is proper and has finite variances. We investigate the numerical performance through simulation and empirical studies.     

Minimax D-optimal designs of contingent valuation experiments: willingness to pay for environmentally friendly clothes

This paper demonstrates how to plan a contingent valuation experiment to assess the value of ecologically produced clothes. First, an appropriate statistical model (the trinomial spike model) that describes the probability that a randomly selected individual will accept any positive bid, and if so, will accept the bid A, is defined. Secondly, an optimization criterion that is a function of the variances of the parameter estimators is chosen. However, the variances of the parameter estimators in this model depend on the true parameter values. Pilot study data are therefore used to obtain estimates of the parameter values and a locally optimal design is found. Because this design is only optimal given that the estimated parameter values are correct, a design that minimizes the maximum of the criterion function over a plausable parameter region (i.e. a minimax design) is then found.     

Improved estimators for the common mean and ordered means of two normal distributions with ordered variances

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959). Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is discussed.     

A NOTE ON ESTIMATING THE LOCATION AND SCALE PARAMETERS OF THE EXPONENTIAL DISTRIBUTION FROM A CENSORED SAMPLE

   
Replacing f (x)/F (x) by α+β(x- θ)/σ in the maximum likelihood equations ∂L/∂θ and ∂L/∂σ calculated from a censored sample, a pair of estimators θ^e and σ^e, is obtained. The variances and covariances of these estimators are calculated and compared with the corresponding values for the best linear unbiassed (BLU) estimators.     

Correlation and efficiency of propensity score-based estimators for average causal effects

Propensity score-based estimators are commonly used to estimate causal effects in evaluation research. To reduce bias in observational studies, researchers might be tempted to include many, perhaps correlated, covariates when estimating the propensity score model. Taking into account that the propensity score is estimated, this study investigates how the efficiency of matching, inverse probability weighting, and doubly robust estimators change under the case of correlated covariates. Propositions regarding the large sample variances under certain assumptions on the data-generating process are given. The propositions are supplemented by several numerical large sample and finite sample results from a wide range of models. The results show that the covariate correlations may increase or decrease the variances of the estimators. There are several factors that influence how correlation affects the variance of the estimators, including the choice of estimator, the strength of the confounding toward outcome and treatment, and whether a constant or non-constant causal effect is present.