On estimating the mean of the selected normal population under the LINEX loss function

Following Parsian and Farsipour (1999), we consider the problem of estimating the mean of the selected normal population, from two normal populations with unknown means and common known variance, under the LINEX loss function. Some admissibility results for a subclass of equivariant estimators are derived and a sufficient condition for the inadmissibility of an arbitrary equivariant estimator is provided. As a consequence, several of the estimators proposed by Parsian and Farsipour (1999) are shown to be inadmissible and better estimators are obtained. Received January 2001/Revised May 2002     

Randomized response: Estimating mean square errors of linear estimators and finding optimal unbiased strategies

Summary General procedures are described to generate quantitative randomized response (RR) required to estimate the finite population total of a sensitive variable. Permitting sample selection with arbitrary probabilities a formula for the mean square error (MSE) of a linear estimator of total based on RR is noted indicating the simple modification over one that might be based on direct response (DR) if the latter were available. A general formula for an unbiased estimator of the MSE is presented. A simple approximation is proposed in case the RR ratio estimator is employed based on a simple random sample (SRS) taken without replacement (WOR). Among sampling strategies employing unbiased but not necessarily linear estimators based on RR, certain optimal ones are identified under two alternative models analogously to well-known counterparts based on DR, if available. Unlike Warner’s (1965) treatment of categorical RR we consider quantitative RR here.     

Simultaneous estimation after selection and ranking and other procedures: The negative exponential case

We considerk (≥2) independent negative exponential populations with unknown location parameters and unknown but equal scale parameter. We incorporate the existing purely sequential and three-stage sampling procedures for selecting the “best” population and study the asymptotic second-order characteristics of the proposed fixed-size simultaneous confidence regions for the location parameters constructed after selection and ranking. Some direct estimation procedures have also been discussed.     

Shrinkage estimation of <Emphasis Type="Italic">P</Emphasis>(<Emphasis Type="Italic">X</Emphasis><<Emphasis Type="Italic">Y</Emphasis>) in the exponential case with common location parameter

We consider the problem of estimating R=P(X<Y) where X and Y have independent exponential distributions with parameters and respectively and a common location parameter . Assuming that there is a prior guess or estimate R₀, we develop various shrinkage estimators of R that incorporate this prior information. The performance of the new estimators is investigated and compared with the maximum likelihood estimator using Monte Carlo methods. It is found that some of these estimators are very successful in taking advantage of the prior estimate available.Acknowledgments. The authors are grateful to the editor and to the referees for their constructive comments that resulted in a substantial improvement of the paper.     

Rough-and-ready assessment of the degree and importance of smoothing in functional estimation

In nonparametric estimation of functionals of a distribution, it may or may not be desirable, or indeed necessary, to introduce a degree of smoothing into this estimation. In this article, I describe a method for assessing, with just a little thought about the functional of interest, (i) whether smoothing is likely to prove worthwhile, and (ii) if so, roughly how much smoothing is appropriate (in order-of-magnitude terms). This rule-of-thumb is not guaranteed to be accurate nor does it give a complete answer to the smoothing problem. However, I have found it very useful over a number of years; many examples of its use, and limitations, are given.     

A note on three-stage confidence intervals for the difference of locations: The exponential case

Fixed-width confidence intervals for the difference of location parameters of two independent negative exponential distributions are constructed via triple sampling when the scale parameters are unknown and unequal. The present three-stage estimation methodology is put forth because (i) it is operationally more convenient than the existing purely sequential counterpart, and (ii) the three-stage and the purely sequential estimation techniques have fairly similar asymptotic second-order characteristics.     

Pitfalls in estimating the X-factor: The case of energy transmission regulation in Brazil

In Brazil, which has one of the biggest energy systems in the world, the National Electricity Regulatory Agency (Agência Nacional de Energia Elétrica – ANEEL) regulates the generation, transmission, distribution and commercialization of electricity. As a key step in running the incentive regulation regime, the regulator applies a DEA-based Malmquist index for estimating the X-factor, which reflects productivity gains that can be expected across all companies involved in the industry. This paper investigates the way the X-factor was estimated in 2015 by ANEEL in the transmission sector concerning the review period 2009–2014. The regulator applies a modified version of the Malmquist index developed by Ray and Desli [1] and also adapts the bootstrapping method of Simar and Wilson [2] to generate confidence intervals for an estimate of the X-factor. Analyzing ANEEL's approach, we have discovered a number of serious analytical and computational shortcomings, which we demonstrate in the paper. On this basis, we address the effect of the estimated X-factor on social welfare, having the final customers to pay a higher price for electricity than they were supposed to.