Calcutta Statistical Association Bulletin, Ahead of Print.
We propose two methods for benchmarking the observed best predictor (OBP; Jiang et al.[]) in small area estimation under the Fay-Herriot model. Furthermore, we propose two methods for estimating the mean squared prediction error (MSPE) of the benchmarked OBP. Theoretical and empirical properties of the benchmarked OBP as well as its MSPE estimators are studied. A real-data example is considered.AMS 2000 subject classification: 62J05
Category Archives: Calcutta Statistical Association Bulletin
Asymptotic UMVUE: Asymptotic Moments Matching the UMVUE under the Ewens Sampling Formula
Calcutta Statistical Association Bulletin, Ahead of Print.
The Ewens sampling formula is a distribution related to the random partition of a positive integer. In this study, we investigate the issue of non-existent solutions in parameter estimation under the distribution. We derive the first and second moments matching estimators to the uniformly minimum variance unbiased estimator (UMVUE) in the asymptotic sense (hereafter referred to as Asymptotic UMUVE) using the Ewens sampling formula. A Monte Carlo simulation study is performed to evaluate the efficiency of the resulting estimators.AMS 2000 subject classification: 62F12, 62P25
The Ewens sampling formula is a distribution related to the random partition of a positive integer. In this study, we investigate the issue of non-existent solutions in parameter estimation under the distribution. We derive the first and second moments matching estimators to the uniformly minimum variance unbiased estimator (UMVUE) in the asymptotic sense (hereafter referred to as Asymptotic UMUVE) using the Ewens sampling formula. A Monte Carlo simulation study is performed to evaluate the efficiency of the resulting estimators.AMS 2000 subject classification: 62F12, 62P25
On Certain Classes of Rectangular Designs
Calcutta Statistical Association Bulletin, Volume 75, Issue 1, Page 72-96, May 2023.
Rectangular designs are classified as regular, Latin regular, semi-regular, Latin semi-regular and singular designs. Some series of self-dual as well as α–resolvable designs which belong to the above classes are obtained. The building blocks of the designs are square (0, 1)-matrices. It is more general to view a class of designs based on an array than to view them based on disjoint groups of treatments of equal size. This generality enabled us to identify three subclasses of rectangular designs: Latin regular RDs, Latin semi-regular RDs and semi-regular L2-type designs which deserve further study. In every construction we obtain a matrix N with square (0, 1)-submatrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well-known tactical decomposition of the incidence matrix of a known design. The authors have already obtained some series of Group Divisible and L2-type designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al.[] The rectangular designs constructed here are of statistical as well as combinatorial interest.AMS Subject Classification: 62K10, 05B05
Rectangular designs are classified as regular, Latin regular, semi-regular, Latin semi-regular and singular designs. Some series of self-dual as well as α–resolvable designs which belong to the above classes are obtained. The building blocks of the designs are square (0, 1)-matrices. It is more general to view a class of designs based on an array than to view them based on disjoint groups of treatments of equal size. This generality enabled us to identify three subclasses of rectangular designs: Latin regular RDs, Latin semi-regular RDs and semi-regular L2-type designs which deserve further study. In every construction we obtain a matrix N with square (0, 1)-submatrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well-known tactical decomposition of the incidence matrix of a known design. The authors have already obtained some series of Group Divisible and L2-type designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al.[] The rectangular designs constructed here are of statistical as well as combinatorial interest.AMS Subject Classification: 62K10, 05B05
Validity Index for Clustered Data in Non-negative Space
Calcutta Statistical Association Bulletin, Volume 75, Issue 1, Page 60-71, May 2023.
We propose a novel nonparametric cluster validity index which can be used to evaluate the unknown number of existing clusters prevailing a data set, to assess the quality of classification for a clustered set of data members, or to compare the clustering output obtained from different algorithms. Our efficient measure depends only on the observation-wise distances of the non-negative clustered data from their origin given in an arbitrary dimensional space. Its fast implementation makes it appealing for big data analysis, whereas the high-dimensional applicability widens its usefulness. Easy interpretation, simple algorithm, speedy computation and great performance, shown in terms of data study, establish our advised validity index as a strong cluster accuracy measure among the acknowledged ones from the literature.AMS subject classification: 62H30
We propose a novel nonparametric cluster validity index which can be used to evaluate the unknown number of existing clusters prevailing a data set, to assess the quality of classification for a clustered set of data members, or to compare the clustering output obtained from different algorithms. Our efficient measure depends only on the observation-wise distances of the non-negative clustered data from their origin given in an arbitrary dimensional space. Its fast implementation makes it appealing for big data analysis, whereas the high-dimensional applicability widens its usefulness. Easy interpretation, simple algorithm, speedy computation and great performance, shown in terms of data study, establish our advised validity index as a strong cluster accuracy measure among the acknowledged ones from the literature.AMS subject classification: 62H30