Calcutta Statistical Association Bulletin

Convergence properties are established for the output of a deterministic Robbins- Monro recursion whose function can have singularities and multiple zeros. Our analysis is built largely on slight adaptations of some lemmas and proofs of Fradkov published only in an untranslated Russian monograph (Derevitzkii and Fradkov , 1981). A gap in Fradkov's proof of the final lemma is fixed but only for the scalar case. Our results can be applied to results of Cantor (2001) to establish the convergence of two well-known time series model recursive estimation schemes in the case of an incorrect moving average model. For such models, it is known that maximum likelihood estimates can converge w .p.1 to a set of values rather than to a single value. When the limit set is finite, our results show that , on a given realization of the time series, the (recursive) estimates will converge to single value. This is the first result establishing that estimates of a moving average coefficient do not oscillate forever among different limit set values when there are more than one.

Full or partial information about the marginals and conditionals of a bivariate distribution is likely to be incompatible. Additionally, information may come from heterogenous sources with limited agreement between sources. Some strategies for selecting a single “minimally incompatible” joint distribution are surveyed.

An eyewitness's description of a missing criminal, for example, is very crucial for apprehending the individual. But, some accounts may be unreliable if it turned out that the witness was ‘far away’ from a crime scene. Estimation of the perception of “distance” can be an important input in many situations including this one.

We ran a number of designed experiments, collected data, and analyzed them in order to understand how individuals perceived “distance”. These experiments and associated data analyses have some clear messages: When a subject was asked to guess the length of an object such as a straight line or a ruler, we found time and again that one's answer routinely depended upon (i) presence or absence of landmarks or reference points, and (ii) what one had thought that was being shown rather than what the true item really was. More investigations in experimental psychology are deemed essential in one's thorough understauding of human perception of “distance”.

This paper develops Bayesian function estimation on compact Riemannian manifolds. The approach is to combine Bayesian methods along with aspects of spectral geometry associated with the Laplace-Beltrami operator on Riemannian manifolds. Although frequentist nonparametric function estimation in Euclidean space abound, to date, no attempt has been made with respect to Bayesian function estimation on a general Riemannian manifold. The Bayesian approach to function estimation is very natural for manifolds because one can elicit very specific prior information on the possible symmetries in question . One can then establish Bayes estimators that possess built in symmetries. A detailed analysis for the 2–sphere is provided.

In the reliability analysis the lack of memory property plays a pivotal role in conceptualizing some life distribution classes and in unique determination of the exponential distribution. On the other hand quite a few results like constancy of the coefficient of variation of the residual life, linearity of the mean residual life characterize the exponential distribution along with the Lomax distribution. Question that arises is - can there be an extended version of the lack of memory property to tie together the exponential and the Lomax distributions through characterization. The present paper presents an affirmative claim and extends the lack of memory property based on standardization technique. It also presents a stochastic version of this extended property with unique determination of the same life distributions. Attempts have also been made to define this extended lack of memory property in the bivariate set up and indicate the bivariate distributions that satisfy the same.

Rosenbaum (1996) and Hedayat and Stufken (1999) considered the construction of compound orthogonal arrays for the two-level factors which are useful in the study of dispersion experiments, pioneered by Taguchi (1986). This paper provides a general method of constructing such arrays and their applications to obtain several asymmetric compound orthogonal arrays for mixed level dispersion experiments. Such arrays are also found to be universally optimal even if the model includes some more parameters.

It is a practical problem to suitably estimate a finite population total providing an estimate of its measure of error when a sample is taken in multistages but some of the chosen first-stage units cannot be covered. Presuming the misses to occur at random, certain estimators of total along with estimators of their measures uf error are derived covering varying probability sampling.

Under the standard model and using an approximate design theory approach, we give necessary and sufficient conditions for a repeated measurements design to be universally optimal for residual effects. In exact design theory, it is shown that symmetric optimal designs can be derived from a single linear equation. Examples of optimal designs, which can be obtained from these conditions, are given. Many of the existing optimal designs, together with new ones, can be obtained by this method. Bounds are given for computing the efficiencies of designs for estimating residual effects.

In this paper Latin Square type association scheme has been generalized and on the basis of this association scheme, a class of designs having orthogonal factorial structure and partial balance has been introduced. Some of its wmbinatorial properties have also been studied.

The fundamental idea of kernel smoothing technique can be recognized as one-parameter data perturbation with a smooth density. The usual kernel density estimates might not match arbitrary sample moments calculated from the unsmoothed data. A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation. It is shown that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments. Moreover, the pointwise rate of MISE of the resulting density estimates remains optimal. Relevant simulation studies are carried out to demonstrate the usefulness and other features of this technique.

The field of Information Technology (IT) has provided extraordinary job growth in the United States over the last two decades; however, women and some minority groups are severely underrepresented in IT occupations, especially in management positions. These groups also on average receive lower salaries than their counterparts. The U.S. National Science Foundation's SESTAT database is created from biennial nationally representative surveys of U.S. scientists and engineers. SESTAT provides detailed information, such as employment history, educational background, and demographic characteristics. These data are analyzed here using latent class analysis, which is an exploratory technique that can be used to cluster cases based on categorical variables. The data are from the 1997 Survey of Doctoral Recipients. The subset of respondents received Ph.D.'s between 1990 and 1996 in either than physical or biological sciences or in engineering and work at higher educational institutions. There are a few significant differences between men and women in desired work activities, job search resources, and adequacy of doctoral training. There are many large, significant differences in limitations when searching for a job, work activities, and family and career status. Latent class analysis helped identify important subgroups of females and males based on clustering simultaneously on several categorical variables.

Functional brain images arc extraordinarily rich data sets that reflect brain function such as cerebral blood flow. These images are widely applied to study brain activity after drug administration or in response to perceptual and cognitive stimuli. Positron Emission Tomography (PET) constitutes one important modality that provides functional brain images. Spatial and temporal patterns in brain activities captured from these images have helped to better understand brain dysfunction in disease and aid in diagnosis and treatment of diseases including ncurogenerative disorders. As PET provides maps consisting of average levels of activity for cuboidal voxels of tissue, it is a substantial analytic challenge to integrate the temporal, spatial and statistical signals making up these data. This paper presents a comparative analysis of three voxel-based methods for characterization of spatial-temporal patterns provided by PET images of cerebral blood flow . The methods are: (i) statistical parametric mapping (SPM) providing a voxel-wise brain map of a selected statistic; (ii) multivariate analysis of covariance jointly with canonical variate analysis (MANCOVA-CVA) identifying regions of the brain that are most responsible for global statistical significance; and (iii) partial least squares (PLS) that uses a path modeling technique with latent variables for dimension reduction. The methods are illustrated using data from sequential H 2 15   O PET studies in baboons to examine whether amphetamine affects relative cerebral blood flow (rCBF) differentially over time and over different regions of brain. The results are found to be consistent across the three methods.

Growing importance of reversed hazard rate (RHR) and inactivity time, as measures of the life distributions, can be noticed from the recent literature on survival and reliability analysis. Keeping in mind tilis special role of RHR and the mean inactivity time, we have made an attempt to define different classes of distributions and study their implicative relationships. A probability bound has also been proposed for the increasing RHR class of distributions.

Generalized linear models are used to analyze a wide variety of discrete and continuous data with possible overdispersion under the assumption that the data follow an exponential family of distributions. The violation of this assumption may have adverse effects on the statistical inferences. The existing goodness of fit tests for checking this assumption are valid only for a standard exponential family of distributions with no overdispersion. In this paper, we develop a global goodness of fit test for the general exponential family of distributions which may or may not contain overdispersion. The proposed statistic has asymptotically standard Gaussian distribution which should be easy to implement.

The classification problem is concerned with allocation of new observations on several variables to two or more distinct categories known to exist a priori, on the basis of some pre-solved cases. Most of the existing solutions to the problem lack detailed inference with respect to the outcomes of the concerned random experiment. An alternative procedure is therefore suggested from frequentist viewpoint, involving relative credentials placed on the different candidate groups in terms of betting odds. The underlying theory was introduced in Chatterjee and Chattopadhyay(1993), the present study being an app lication towards the classification problem. Performance of the proposed ruie has been studied for some real-life examples through discriminant analysis.

Upper weak record values from a sequence of independent identically distributed random variables are considered. Several distributional properties of the upper weak records from geometric distribution are presented. Based on these distributional properties some characterizations of the geometric distribution are given.

A unit is to be classified into one of two correlated homoscedastic normal populations by W classification statistic. The two populations are like two different states of a disease. A sample unit can be observed in both the states (populations) . The observations made on the same unit in the two populations are correlated. W is based on an unmatched training sample where N sample units are observed in both the populations and N_i- N units are observed in population i, i = 1, 2. The exact density of W in such set up is derived for unknown means and common dispersion matrix where the correlation linking the populations is known or unknown. Simulated density of W is plotted and probability of correct classification (PCC) is evaluated using simulation.