Estimating parameters of a selected Pareto population

Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

“…However, it can be estimated using method available in van Zyl (2015) or Tripathi et al (2015), if needed. As a comparison with the results for symmetric loss functions, Misra and van der Meulen (2001) and Kumar and Gangopadhyay (2005) theoretically proved that the natural estimator based on the best equivariant estimator, γ −2 γ −1 Y k , dominates the other natural estimators under the squared error loss function. We have provided formulae as well as compared the risk-bias and risk of alternative estimators with simulation so that the researchers and users could use an appropriate estimator to achieve their goals under varying conditions.…”

“…The performances of the UMVUE and the natural estimators were also compared. Kumar and Gangopadhyay (2005) derived the UMVUE and also constructed an admissible class of linear estimators for k = 2. They also proved a general inadmissibility result for the scale equivariant estimators.…”

Simultaneous estimation of Poisson means of the selected subset

“…The problem of estimating a characteristic(s) of the selected population(s) corresponding to the continuous case has been studied in detail in the literature. Some recent references include Kumar and Kar (2001), Kumar and Gangopadhyay (2005), Misra and Meulen (2003), Parsian and Farsipour (1999), Sill and Sampson (2007) and Vellaisamy (2009). The estimation after subset selection for continuous populations has been considered by Panchapakesan (1984, 1986), and Vellaisamy (1992Vellaisamy ( , 1996, among others.…”

A note on unbiased estimation following selection

“…See, for some recent works and related References, [1][2][3][4]. Suppose a component is selected from the competing k brands and is used as a component of a larger system.…”