Calcutta Statistical Association Bulletin

Histone modifications (HMs) are an important post-translational feature. Different types of HMs are believed to co-regulate biological processes such as gene expression, and are therefore intrinsically dependent on each other. We develop inference for this complex biological network of HMs based on a graphical model for the dependence structure across HMs. We report inference on HM dependence in a case study with ChIP-Seq data from a next-generation sequencing experiment. A hierarchical model extension allow us comparison of multiple graphs corresponding to different genomic regions. The described inference is an important step towards cracking the histone code.

Search designs form an indispensable tool under model uncertainty. However, the progress in this area has been limited due to com- plexities of checking the necessary rank condition for search designs. Designs for searching two two-factor and one three-factor interaction effects under a tree structure in the presence of the general mean and all the main effects are provided here. These designs are obtained under the assumption that four-factor and higher order interaction effects are all absent. Probability of correct searching obtained through simulations is also discussed.

The linear mixed model, with its combination of fixed and random parameters, plays a central role in many statistical applications. Here we review results on conditions for best linear unbiased estimates (BLUEs) of estimable functions of fixed parameters under one linear mixed model to remain BLUEs under a second model, which difiers from the first in covariance structure. Without making full rank assumptions for design matrices or covariance matrices, we also review results for the conditions under which best linear unbiased predictors (BLUPs) of random parameters under the first model remain BLUPs under the second model, and for the conditions under which both BLUEs and BLUPs under the first model remain the BLUEs and BLUPs under the second. We also provide a rather generous list of related references.

Factorial designs are commonly used to assess the impact of factors and factor combinations in industrial and agricultural experiments. Though preferred, complete randomization of trials is often infeasible, and randomization restrictions are imposed. In this paper, we discuss a finite projective geometric (PG) approach to unify the existence, construction and analysis of multistage factorial designs with randomization restrictions using randomization defining contrast subspaces (or flats of a PG). Our main focus will be on the construction of such designs, and developing a word length pattern scheme that can be used for generalizing the traditional design rank- ing criteria for factorial designs. We also present a novel isomorphism check algorithm for these designs.

Kiefer and Wynn (1981) developed optimality properties of 1st Order neighbor balanced designs. These neighbor balanced designs require a large number of blocks, specially, for even number of treatments. Construction of block designs for even number of treatments with correlated observations with lesser number of blocks is a challenge to researchers. In the present paper, an attempt has been made to construct efficient designs with even number of treatments in lesser number of blocks considering the observations, correlated of 1st order neighbors. The general efficiency balanced (GEB) block designs (Das and Ghosh, 1985 and Kageyama and Mukerjee, 1986) with correlated observations have been constructed for even number of treatments. The structure of the C-matrix of the design has been derived and the canonical efficiencies, A and D efficiencies of the resultant GEB designs are also obtained for different values of the correlation coefficient ρ (0 ≤ ρ ≤1).

Let {X₁, ...,X _n } be a random sample from a continuous distri- bution F defined on the k−dimensional Euclidean space R^k; for some k≥1. In many statistical applications we are interested in statistical properties of a function h(X₁, ...,X _m ) of m ≥ 1 observations. Frees (1994, J. Amer. Stat. Assoc.) considered estimating the density function g associated with the distribution function

G ( t )   =   P ( h ( X 1 , ... ,   X m )   ≤   t )

using the kernel method. In many applications, though, the functions of interest are non-negative where the usual symmetric kernels applied in the kernel density estimation are not appropriate. This paper adapts the alter- native density estimator developed in Chaubey and Sen (1996, Statistics and Decisions) by smoothing the so called empirical kernel distribution function:

G n ( t )   =   ( m n ) − 1 ∑ ( n , m ) 1 ( h ( X i 1 , X i 2 , ... , X i m ) ≤ t ) ,

where 1(A) denotes the indicator of A and ∑ ( n , m ) denotes sum over all possible ( n m ) combinations. Applications and asymptotic properties of the alternative estimator are investigated.

The purely sequential minimum risk point estimation procedure for the unknown parameter θ (> 0) in a Uniform (0; θ) population has been discussed in this article. This is developed under a squared error loss plus a linear cost function of sampling. The unknown parameter θ is estimated by means of four different estimators in the stopping rule, where as in the loss function two different unbiased estimators of θ are proposed. The unbiased estimators are randomly stopped versions of Χ_n:n and X¯n in either loss function. Performances of such estimators are compared. Clearly, using a randomly stopped version of X¯ _n would amount to some loss of in- formation when compared with a corresponding randomly stopped largest sample order statistic under both loss functions and the stopping rules. In this paper, we explore a novel approach to recover any loss of information by fine-tuning the loss function and then properly tailoring the associated sequential methodologies. We examine how the sequential risks of our newly proposed methodologies would compare with those associated with the ex- isting sequential estimators and illustrate our methodologies with the help of a real dataset.

We consider a specific class of multiple test problems, consisting of M simultaneous point hypothesis tests in local statistical experiments. Under certain structural assumptions the global hypothesis contains exactly one element ϑ^* (say), and ϑ^* is least favourable parameter configuration with respect to the family-wise error rate (FWER) of multiple single-step tests, meaning that the FWER of such tests becomes largest under ϑ^*. Further-more, it turns out that concepts of positive dependence are applicable to the involved test statistics in many practically relevant cases, in particular, for multivariate normal and chi-square distributions. Altogether, this allows for a relaxation of the adjustment for multiplicity by making use of the intrinsic correlation structure in the data. We represent product-type bounds for the FWER in terms of a relaxed Šidák-type correction of the overall significance level and compute “effective numbers of tests”. Our methodology can be applied to a variety of simultaneous inference problems for multi-dimensional (location) parameters, as frequently occurring in analysis of variance models or in the context of simultaneous categorical data analysis. For example, simultaneous chi-square tests for association of categorical features are ubiquitous in genetic association studies. In this type of model, Moskvina and Schmidt (2008) gave a formula for an effective number of tests utilizing Pearson's haplotypic correlation coeffcient as a linkage disequilibrium measure. Their result follows as a corollary from our general theory and will be gen- eralized.

We prove that under very mild assumptions, the estimated class boundaries for the method of Likert-type scaling are Best Asymptotic Normal estimators of the true values. Also, we show that in the situation where the number of categories increases with sample size, the estimates are uniformly consistent under suitable conditions.

Clustering and classification of difierent astronomical objects have become one of the most important area in the field of Astrostatistics. The basic objective of cluster analysis is related to segmentation of a collection of objects into a number, may be unknown, of clusters such that objects in the same cluster are more closely related than those assigned to different clusters. Various methods are available for clustering, which may be broadly categorized under supervised and unsupervised learning. In case of supervised learning there are some input variables, called predictors and also some output variables, called responses. But in case of unsupervised learning only predictors are under consideration in the absence of responses. Under both the above mentioned categories, for clustering and classification, several methods have been developed on the basis of the underlying nature of data sets. However, there is no well known criteria to compare the performances of difierent techniques. The present paper is an attempt to compare the appli- cability of some of the clustering techniques on the basis of Gaussian and non Gaussian astronomical data sets. A post classification technique is used as a supervised learning to justify the robustness of the variety of unsupervised methods used in this purpose. Finally the similarity of clusters, obtained from different methods, is viewed in terms of astrophysical properties of the objects grouped in different clusters.

The classical approach of stochastic modeling is to first guess a model and then to validate the same using observed data and some test for goodness of fit. Unfortunately, this is not a very rational approach. The initial choice of model becomes a subjective one, some goodness of fit test may demand for large number of observations and difierent models may fit well for the same data set. Given these limitations of the classical approach, one may, as an alternative, make use of characterization results. At the same time, to take care of the difficulties in verification of characterizing properties one needs stability properties as well.

Stability results have been mostly studied for the exponential distribution. So far as non-exponential distributions are concerned, one may refer to only few works. The present study deals with stability properties in terms of Matusita distance for characterization results involving reliability measures. These results are generic in nature and can be used for the distribution cor- responding to any non-negative random variable.

A Generalized Process Capability Index, defined as the ratio of proportion of specification conformance (or, process yield) to proportion of desired (or, natural) conformance, has been developed by Maiti et al.(2010). Almost all the process capabilities defined in the literature are directly or indirectly associated with this generalized index. In this article, a loss function has been attached to the product quality characteristic for deviation from its target to define the index named as generalized quality capability index. Symmetric as well as asymmetric loss functions have been considered. We deal with the index in case of normal, non-normal and discrete processes. An algorithm for determining optimum process center for an off-centered process has been prescribed. A process data set has been analyzed.

In this paper we apply statistical classification techniques to a case-control study. The data analysed relates to Acute Coronary Syndrome (ACS). We discuss an adaptation of the Naive Bayes method, and assess the results using an analysis of deviance based approach. Analysis of deviance is used to rank the driver variables, such as phenotype and genotype variables to their relative contribution to classify a new case into one of ACS or non-ACS group. Results from the case-study reveal that a combination of Single Nucleotide Polymorphism (SNP) 2 and Single Nucleotide Polymorphism 4 is the most important, and the aggregation of platelets on addition of Adenosine-di-phosphate along with nano particles the next most important factors in classifying an unseen patient into one of the two groups. Some limitations and future analyses are also discussed.

Geometric stable distributions received much attention in recent years and their applications in different fields ranging from reliability to financial mathematics are well established by several researchers. It can be used in modeling peaked and heavy tailed observations that may be a result of a random number of independent innovations. Although the theory and applications of geometric stable distributions are well developed and appeared in many literature in recent years, their applications in time series modeling are not developed. Present work aims at developing autoregressive model using geometric stable distributions as marginal distributions.