Constantinos Petropoulos

A CLASS OF IMPROVED ESTIMATORS FOR THE SCALE PARAMETER OF AN EXPONENTIAL DISTRIBUTION WITH UNKNOWN LOCATION

ABSTRACT Under quadratic loss, a class of improved estimators for the scale parameter of an exponential distribution with unknown location is constructed. The method is analogous to Maruyamas (Minimax Estimators of a Normal Variance. Metrika 1998, 48, 209–214) construction for the variance of a normal distribution.

Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

Estimation of the quantile μ + κσ of an exponential distribution with parameters (μ, σ) is considered under an arbitrary strictly convex loss function. For κ obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when κ exceeds a lower bound specified below, a new minimax estimator is identified.

Estimation of the parameters of an exponential distribution under constrained location

In this paper, the problem of estimating parameters of an exponential population is studied under quadratic loss functions. The location parameter of the distribution is assumed to be bounded above by a known constant. Various classes of estimators are derived using integral expression of risk difference (IERD) method of Kubokawa (1994). Some complete class results are also established.

A Class of Improved Estimators for the Scale Parameter of a Mixture Model of Exponential Distribution with Unknown Location

Under Steins loss, a class of improved estimators for the scale parameter of a mixture of exponential distribution with unknown location is constructed. The method is analogous to Maruyamas (1998) construction for the variance of a normal distribution and also an extension of the result produced in Petropoulos and Kourouklis (2002). Also, robustness properties are considered.

Estimating a linear parametric function of a doubly censored exponential distribution

ABSTRACT For an arbitrary strictly convex loss function, we study the problem of estimating a linear parametric function is a known constant, when a doubly censored sample is available from a two-parameter exponential population. We establish the inadmissibility of the best affine equivariant (BAE) estimator by deriving an improved estimator. We provide various implications for quadratic and linex loss functions in detail. Improvements are obtained for the absolute value loss function as well. Further a new class of estimators improving upon the BAE estimator is derived using the Kubokawa method. This class is shown to include some benchmark estimators from the literature.

Estimation of the shape parameter of a Pareto distribution

ABSTRACT We consider the problem of estimating the shape parameter of a Pareto distribution with unknown scale under an arbitrary strictly bowl-shaped loss function. Classes of estimators improving upon minimum risk equivariant estimator are derived by adopting Stein, Brown, and Kubokawa techniques. The classes of estimators are shown to include some known procedures such as Stein-type and Brewster and Zidek-type estimators from literature. We also provide risk plots of proposed estimators for illustration purpose.

Minimax estimators for the lower-bounded scale parameter of a location-scale family of distributions

ABSTRACT This article is concerned with the minimax estimation of a scale parameter under the quadratic loss function where the family of densities is location-scale type. We obtain results for the case when the scale parameter is bounded below by a known constant. Implications for the estimation of a lower-bounded scale parameter of an exponential distribution are presented under unknown location. Furthermore, classes of improved minimax estimators are derived for the restricted parameter using the Integral Expression for Risk Difference (IERD) approach of Kubokawa (1994). These classes are shown to include some existing estimators from literature.