bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Optimal Selection Procedures for Dependent Normal Populations
Authors: Hsu Tong—An
Published: August 2016

We consider k dependent normal populations having known equal variance. The problem is to select the population associated with the largest mean. Let π1, ..., πk be k populations. We assume that the random variable Xi associated with πi ( i = 1, ..., k). Let X1, ..., Xk be k—variate normal distribution with unknown mean μ1, ... , μk and with equal variance σ2 and with correlation matrix { ρi j} For two case : (a) ρi j = aiaj for i ≠ j and (b) ρi j = ρ, for i ≠ j, we construct some optimal subset selection procedure to select a subset of the k dependent normal population containing the largest population mean.

AMS ( 1980) subject classification : Primary 62F07 ; Secondary 62030
Detailed Statistical Inference—An Alternative Non-Bayesian Approach : Two-Decision Problem
Authors: Chatterjee Shoutir Kishore , Chattopadhyay Gaurangadeb
Published: August 2016

In this paper we propose a new approach to detailed inference for any two-decision problem under the frequentist framework, based on a somewhat different interpretation of the confidence coefficients in terms of betting odds. We first elaborate this interpretation with reference to summary inference and enlarge the interpretation to the needs of detailed inference. The actual application of the proposed technique requires the choice of some suitable utility functions. We illustrate our ideas through some examples.

AMS Subject Classification: 62 A 99.
On the Performance of a Test for Coefficient of Variation
Authors: Rao K. Aruna , Vidya R.
Published: August 2016

Approximate standard errors (s.e) of sample coefficient of variation (c.v.) are available in the literature (Kendall and Stuart, 1977; Serfting 1980). Using these s.e.'s a large sample test can be constructed to test for the specified value of population c.v. The test can also be justified on the principles of Wald test. These s.e.'s have been worked out assuming that the random variable has a distribution. Following Foutz and Srivastava (1977), we study the asymptotic performance of the test when the model is incorrect. Examples from realistic situations have been considered and approximate Babadur efficiencies have been worked out. Numerical results indicate that the test is fairly robust when the departure from the model is not too pronounced.
Efficiency-⁄Partially-Efficiency-Balanced Block Designs through Difference Sets
Authors: Tyagi B.N. , Rizwi S. K. H.
Published: August 2016

In this paper, some new efficiency⁄partially efficiency Balanced block designs have been constructed using the method of differences. These designs are binary with incomplete blocks and are of much practical utility.
On Common Location of Several Exponentials under a Class of Convex Loss Functions
Authors: Jin Chun , Pal Nabbndu
Published: August 2016

In this paper we address the problem of estimation of the common location parameter of several exponential distributions. We assume that the scale parameters are all unknown and possibly unequal. From a decision theoretic point of view we suggest a wide class of estimators dominating the maximum likelihood estimator (MLE) under a class of convex loss functions.
Selection Procedures for Location Parameters Based on Two-Sample U-Statistics
Authors: Kumar Narinder , Gill Amar Nath , Mehta Gobind P .
Published: August 2016

Let π1, ... , πk be k independent populations and let Fi ( x)= F( x - θi) be the absolutely continuous cumulative distribution function (cdf) of the i-th population indexed by the location parameter θi; i=1,,.... k. A class of subset selection procedures based on sub-sample extrema for unequal sample sizes is proposed for the problem of selecting a subset from ( π1, .... πk) which contains the population with largest location parameter. The proposed subset selection procedures are then compared with the subset selection procedures of Hsu (1981) in the sense of Pitman ARE (asymptotic relative efficiency). It is shown that these procedures can approximately be implemented with the help of existing tables and sample size sufficient for their implementation, based on simulation results, is discussed.

AMS (1980) Subject Classification: Primary 62F07; Secondary 62H10
A Construction of a Resolvable 3-Design
Authors: Meitei K. K. Singh
Published: August 2016

This paper consists of a construction method of resolvable 3-design starting from a 3- ( v, k, λ3 ) design having b = 2( v -1). The new design has smaller block size than tho block size of the parent (starting) design.
An Improved Unrelated Question Randomized Response Strategy
Authors: Mangat Naurang Singh , Singh Ravindra , Singh Sarjinder
Published: August 2016

We consider the problem of estimating π the proportion of human population belonging to the sensitive category. A new randomized response procedure using known πr (the proportion of population possessing a non-stigmatized attribute) bas been proposed. The proposed strategy provides unbiased and more efficient estimator of π than the one based on Greenberg et al.'s (1969) usual unrelated question randomized response model with known πr
Estimation of the Probability of Discovering a New Category in Finite Population Sampling
Authors: Sinha Bikas K. , Sengupta S.
Published: August 2016

Considered is the set-up of sampling from a finite population of N (known) units divided into k (unknown) mutually exclusive and exhaustive categories, the ith category possessing N i, (unknown) units, 1 ⩽ i ⩽ k As and when sampling is terminated, some categories may remain undiscovered. A quantity of interest is the probability of discovering a new category when an additional draw is made. We address the problem of estimation of this unknown probability and also that of more general parametric functions. Simple random sampling (with/without replacement) is discussed.
Construction of Generalized Cyclic Combinatorially Balanced Designs for First Order Residual Treatment Effects
Authors: Vartak M.N. , Mashouri G.H. , Aggarwal M.L.
Published: August 2016

Designs combioatorially balanced for residual treatment effects of various orders, (especialJy first and second orders) with and without interactions were discussed in considerable details by williams (1949). Construction of combinatorially balanced designs for residual treatment effects was also considered by Patterson (1952); Hedayat and Afsarinejad (1975, 1978); Cheng and Wu (1980). An excellent account of such designs is given by Jones and Kenward (1989).

In this paper, a method of construction of generalized cyclic designs combinatorially balanced for residual treatment effects of the first order without interactions, is presented. The method is based on an extension of theorems on symmetricaliy repeated difference sets developed by Bose (1939) and others. See Raghavarao (1971) for deiails,

AMS (1980) Subject Classification: Primary 62k99; Secondary 05B10,05B30
A Useful Lemma and its Application to Negative Binomial Distribution
Authors: Hambdani G. G.
Published: August 2016

A useful lemma is established and is used to obtain certain relationships between the parameters and median of a negative binomial distribution,
A General Class of Unbiased Estimators of a Parameter
Authors: Singh Housila P. , Singh Virendra P.
Published: August 2016

In this note an attempt has been made to develop a class of unbiased estimators for an unknown parameter. Several estimators can be shown as a direct result of the proposed class.
Detailed Statistical Inference-multiple Decision Problem
Authors: Chatterjee Shoutir Kishore , Chattopadhyay gaurangadeb
Published: August 2016

The procedure for detailed statistical inference developed by the authors in an earlier paper (1992) for the two-decision case, is extended here to the case of several decisions. Alongwith the rule for choosing the decision, the problem of stating data dependent measures of confidence in terms of betting odds, is considered. The extension involves generalization oftlie coneept of legitimacy of betting odds introduced in the earlier paper and the choice of a suitable utility function for bets. The actual solution is worked out in the case of logarithmic utility. A rather intricate mathematical result requires to be established to prove the existence of an optimum rule in this case. Application of the procedure is illustrated through some numerical examples.
On Shortest Confidence Intervals for Product of Gamma Means
Authors: O'Brien Robert , Sinha Bimal K.
Published: August 2016

In many environmental applications, such as risk and exposure assessment associated with hazardous waste sites, one is interested in a parameter which can be described as the product of means of several independently distributed gamma variables. In this paper an optimal method of constructing a confidence interval for this parameter is developed. Explicit formulae are given in the case of two independent variables, a situation quite eommon in applications. The proposed prodedure provides a substantial improvement over the commonly used technique of combining individual intervals constructed separately for each mean.
A Bayesian Approach to Kalman Filter for Elliptically Contoured Distribution and its Application in Time Series Models
Authors: Basu A. K. , Das J. K.
Published: August 2016

This paper develops a Bayesian formulation of Kalman filter under the errors having elliptically contoured distributions in both observation equation and system (or state) equation, using some recent results in multivariate analysis. Estimation of parameters in case of missing observations and prediction of missing observations as well are dealt with under the above set up of autoregressive-moving average process in time series. Two illustrative examples are presented with the help of AR(1) model and ARMA (1, 1) model.
The Neyman-Scott Phenomenon in Generalized Linear Models and Overdispersed Exponential Families
Authors: Bhanja Joydeep , Ghosh Malay
Published: August 2016

In fixed effects balanced one-way analysis of variance models with homoscedastic normal errors, the maximum likelihood estimator (MLE) of the error variance is inconsistent as the cell-size remains fixed but the number of cells grows to infinity. This is the famous Neymnn-Scott phenomenon. The present paper shows that the Neyman-Scott phenomenon continues to hold for estimating the scale parameter in the canonical version of generalized linear models when the number of nuisance parameters grows to infinity. A similar result holds for overdispersed exponential faruily of distributions. It is also pointed out how the conditional MLE in such cases does not suffer from the inconsistency problem. The relationship between the conditional score function and the corrected score function in general mixture models is also pointed out. The Neyman-Scott phenomenon is also shown to hold for the two-parameter exponential family typically used for modelling overdispersion.
A Note on the Strong Law of Large Numbers
Authors: Bose Arup , Chandra Tapas K.
Published: August 2016

Let { X n} be a sequence of pairwise independent (or -mixing) mean zero random variables such that [Formula: see text] is integrable on (0,∞) and [Formula: see text] then we show that [Formula: see text] almost surely as n→∞, These are very convenient and immediate generalizations of the classical SLLN for the iid case.
Explicit Stable Strong Laws of Large Numbers
Authors: Adler André
Published: August 2016

In this article it is shown, through a very interesting class of random variables, how one may go about explicitly obtaining constants in order to obtain a stable strong law of large numbers. The question at hand is, not when we can find constants an and bn so that our sequence of i. i.d. random variables obeys this type of strong law of large numbers, but how one goes about constructing these constants so that [Formula: see text] almost surely, even though { X, Xn} are i.i.d. with either [Formula: see text] There are three possible cases. We exhibit all three via a particular family of random variables.
Some Aspects of Forecasting with Vector Moving Average Processes
Authors: Peiris M. Shelton
Published: August 2016

This paper considers forecasts of the sum of a particular component of two independent Gaussian vector moving average processes. The efficiency of forecasts are compared via ( a) the corresponding component models, ( b) the joint vector models and ( c) the combined joint vector model.
Statistics : A Key Technology for Development—How well have We Used the Key ?*
Authors: Parikh Kirit S.
Published: August 2016

I am deeply honoured to be invited to aive the First Soumitra Kumar Chakravarti Memorial Lecture.

Calcutta has been the cradle of statistics in India where many distinguished great statisticians of India have grown. Many of them have been associated with tho Calcutta Statistical Association. I am therefore, particlarly honoured that you have asked me, who is not a statistician by training, to give this Pirst Memorial Lecture, I do hope, the viewpoints of a user of statistics will be found useful.
Some Properties of the Stuttering Poisson Distribution
Authors: Moothathu T. S. , Kumar C. Satheesh
Published: August 2016

Here we establish that the Stuttering Poisson distribution (SPD) is the distribution of the random sum of certain type of independent and identically distributed random variables. The poisson binomial distribution is shown to be a special case of SPD. Further recurrence relations for probabilities and factorial moments of SPD are established.
Quantile Specification Method of Comparison Values in Analytic Hierarchy Process
Authors: Basak Indrani , Basak Prasanta
Published: August 2016

Expert opinions are sought in order to elicit pairwise comparison values of the decision elements in Analytic flierarchy Process (AHP). In this article, we propose an alternative elicitation method. These new elicitations are in terms of a few selected quantiles of the comparison values. A statistical model is provided for processing these elicited values. The advantage of this approach is that one can generate as many pairwise comparison matrices of the decision elements as desired. This allows one to determine whether differences in the final priority scores of the alternatives are statistically significant.
Some Useful Properties of the Bayes Risk in Classification
Authors: Bagui Subhash C. , Datta Somnath
Published: August 2016

In this article we study some properties of the Bayes risk with respect to prior probabilities in the context of two class classification problems. We show that Bayes risk is maximized when the ratio of the prior probabilities equals the median of the likelihood ratio statistic under the average density. We also show that when probability density functions (pdf) are symmetric and differ only in locations and the likelihood ratio is monotonic, the Bayes risk has a unique maximum at prior probability , and decreases as the difference between the prior probabilities increases. Several interesting examples are cited to illustrate the results.
Optimal Fractional Factorial Designs with 18, 34 and 66 Runs
Authors: He Lijian , Jacroux Mike , Yu Lan
Published: August 2016

In this paper, we show how to augment many of the resolution III and IV minimwn aberration two-level fractional factorial designs given in Chen, Sun and Wu (1993) with two additional runs so that a majority of the designs obtained are optimal under models which contain only main effects or estimable main effects and two factor interactions.
Predictive Estimation of Finite Population Variance
Authors: Biradar R.S. , Singh H.P.
Published: August 2016

Adopting predictive approach, estimators are proposed for population variance [Formula: see text] using different predictors for mean and variance of unobserved units in the population. Asymptotic expressions for bias and mean square error of these new estimators are obtained and compared with those of some known estimators of population variance. Predictive character of some known estimators is also examined . An empirical study demonstrated superiority over others of one of the proposed estimators, which uses regression estimators as predictors for mean and variance of unobserved units. Also, one of the other proposed estimators which does not utilize any auxiliary information has been found to be more efficient than the traditional unbiased estimator [Formula: see text].
Utility-Oriented Simpson-Type Indexes and Inequality Measures
Authors: Sen Pranab kumar
Published: August 2016

Measures of economic inequality and poverty indexea are generally baaed on the Gini coefficient and some other measures of income inequality. In a broader context of diversity or distributional inequality, there may be a relatively more prominent qualitative flavour, and in view of that, the Gini-Simpaon index may be appropriate. To blend qualitative and quantitative variations together, some utility-oriented generalizations of the Gini-Simpson index are considered and their general properties are studied. Decomposability properties of such measures are also discussed.
Kullback-Leibler Information type Measure of Departure from Conditional Symmetry and Decomposition of Measure from Symmetry for Contingency Tables
Authors: Tomizawa Sadao , Saitoh Kayo
Published: August 2016

For the analysis of square contingency tables, Tomizawa (1994) and Tobmizawa (1995) considered the Kullback-Leibler (KL) information type measures to represent the degree of departure from symmetry ( S) and from global symmetry ( GS), respectively. This paper proposes a K L information type measure to represent the degree of departure from conditional symmetry (CS), being an extension of S. The proposed measure would be useful for comparing the degree of departure from CS in several tables. Also this paper gives a theorem that the value of measure from S is equal to the sum of the value of measure from GS and that from CS.
On Covariance Analysis in Nested Classification to Study the Fertility Differential in North-Eastern Libya
Authors: Budijaja K.Y. , Bhuyan K.C.
Published: August 2016

Covariance analysis with k concomitant variables in three-stage classification has been presented under usual assumption. The analytical procedure has been utilized to study the fertility variation by socio-economic status of mother nested within her occupation and education. Fertility levels are adjusted for the factors father's education, duration of breast feeding, child mortality and duration of marriage. Firat two factors have declining effects and the last two accelerate the fertility level. Mother's education is most influencing factor to reduce the number of ever born children. However, fertility level, even among educated mothers, can be increased if duration of marriage and child mortality are not reduced and period of breast feeding is not increased.
Opinion Polls and Statistics
Authors: Karandikar Rajeeva L.
Published: August 2016

In this article, several general questions regarding opinion polls and seat prediction in the context of Indian parliamentary democracy are diacussed and the methodology used by the author to tackle these is described. Also included are the results of the opinion polls leading to the 1998 parliamentary polls.
On a Class of Distributions Having Laplace Transforms with Multiple Negative Poles and Complex Zeros
Authors: John K.J. , Nair K.R. Muraleedharan
Published: August 2016

In the present paper we look into certain properties of a class of probability density functions having Laplace transforms with multiple negative poles and complex zeros. Also characterization theorems are formulated for a mixture of gamma distributions in terms of zeros and poles in the Laplace transforms.
Estimation of Common Parameter of Several Exponential Distributions
Authors: Handa B.R. , Kambo N.S.
Published: August 2016

The problem of estimation of common parameter of k exponential distributions with known but possibly unequal coefficients of variation has been solved by showing its structural equivalence with the problem of estimation of parameter of single exponential distribution with weighted average coefficient of variation.
Characterization of Lifetime Distributions Using Measure of Uncertainty
Authors: Sankaran P.G. , Gupta R.P.
Published: August 2016

In the present paper, we characterize exponential, Pareto, Wei bull and beta distributions using the concept of measure of uncertainty defined by Ebrahimi and Pellery (1995). Further, a new measure of uncertainty is introduced and its properties are discussed. Finally, we present a characterization theorem for extreme value distribution by extending the concept into negative set-up.
Construction of Balanced Bipartite Block Designs with Nested Rows and Columns
Authors: Parsad Rajender , Sreenath P.R. , Agrawal Niti
Published: August 2016

This paper provides some methods of construction of Balanced Bipartite Block Designs with Nested Rows and Columns (BBPB-RC Designs). The methods are based on balanced incomplete block (BIB) designs, initial block solutions, merging of treatments and use of reinforcement technique.
Generalised EGD Designs and Orthogonal Factorial Structure
Authors: Adhikary Basudev , Bandyopadhyay Sanjay
Published: August 2016

In this paper we have introduced a class of block designs termed Generalised Extended Group Divisible (GEGD ⁄ 3"-1) P.B.I.B. design which have orthogonal factorial structure. We have also mtroduced the concept of subfactor balance and shown that a sufficient condition for subfactor balance is that the corresponding block design is a (GEGD⁄ 3"-1) P.B.I.B. design.
Bayesian Analysis of Clustered Regression Models for Mixed Discrete and Continuous Outcomes – An Application to Depressive Disorder Data
Authors: Das Kalyan , Rao J.N.K. , Biswas Atanu
Published: August 2016

A computationally practical form of Bayesian analysis for multiple response variables has been applied to data on depressive disorder. The model, considered here, allows for arbitrary covariate effects and also cluster effects through some known link functions. It is quite flexible and is applicable to any clustered data involving polytomous and continuous variables.
The five Faces of Bayesian Statistics
Authors: Cox D. R.
Published: August 2016

A brief review is given of five different interpretations of Bayesian statistical inference.

AMS {2000} Subject Classification: 62A01.
On Stochastic Ordering and a General Class of Poverty Indexes
Authors: Chatterjee Shoutir Kishore , Sen Pranab Kumar
Published: August 2016

Although measures of diversity and inequality have been extensively proposed in socio-economic and health perspectives, violation of a subtle monotonicity criterion (under stochastic ordering) diminishes their rationality and utility in the context of poverty and other ecomomic indexes. A modification is proposed here to develop certain stochastic ordering monotonicity preserving diversity measures that overcome this drawback. Such measures are shown to be invariant under increasing transformation, and thereby appropriate for (partially) ordered categorical response data models.

AMS{2000) Subject Classification: 62H17, 62-07.
Bayesian Nonparametric Estimation of Intensity Functions Using Markov Chain Monte Carlo Method
Authors: Deshpande J.V. , Mukhopadhyay M. , Nimbalkar U.V. Naik
Published: August 2016

Let N( t) be a counting process indicating the failures (and instantaneous repairs) of a repairable system up to time t. We model the probabilistic behaviour of the process by a nonhomogeneous Poisson process (NHHP) with intensity function λ( t). In the absence of any grounds in favour of a specific parametric form for λ( t) we assume that it is constant between failure epochs and at these epochs receives a jump (the damage-atfrulure- model). Again we don't know the heights of these jumps. Therefore we assume a heirarchical Bayes formulation. The heights of the jumps are assumed to have constrained conditional gamma distributions. The hyperparameters of the gamma distribution are assumed to have known uniform distributions. The exact Bayes solutions are analytically intractable. Hence we provide a scheme of simulation via the Metropolis-Hastings algorithm to estimate the features of the posterior distribution. The methodology is illustrated by applying it to a well known data set.

AMS (2000) Subject Classification: Primary 62F15, 62G05; Secondary 65C05.
Network and Adaptive Sampling with Unequal Probabilities
Authors: Chaudhuri Arijit
Published: August 2016

We consider two sample survey situations. In one, we have a list of ‘selection units’ (su's) out of which one may suitably draw a sample. But the interest is to estimate the total value of a variable defined on an unknown number of individuals called ‘observational units’ (ou's) which are not directly identifiable but may be contacted through the above su's to “one or more” of which each ‘ou’ is ‘linked’ in a ‘well-defined’ manner. Each collection of ou's so linked is called a ‘network’. Each network is ‘disjoint’ from every other and together they exhaust all the ou's of interest. Through a sample of su's one may observe the variate-values for the ou's in the networks linked to the sampled su's. This approach of reaching samples of ou's through such networks is called ‘network’ sampling. Thompson (1990, 1992) and Thompson and Seber (1996) have given theories of estimation of total or mean and variance estimation when the su's are selected by simple random sampling (SRS) without replacement (WOR) or by stratified SRSWOR methods. Here we extend to general sampling schemes with unequal probabilities.

In the second kind of surveys an initial sample is chosen from a list of identifiable units for many of which the value of a variable is ‘zero’ and only for a few ‘unknown and unidentified’ units the values are positive. The purpose is to estimate the population total with a high coverage of the positive-valued units in the sample. A concept of a ‘neighbourhood’ is then well defined such that given a unit with a positive value some of those in its neighbourhood may also hopefully be positive-valued. So, from an initial sample one may go on ‘adaptively’ extending it by adding successively to each positive-valued unit in the sample each unit in its neighbourhood and stopping only on encountering a ‘neighbouring’ unit that is zero-valued. The relevant theory is developed in the above locations cited. But this covers only SRS with and without replacement (WR and WOR) for the initial sample. We extend here to more general sampling schemes.

AMS (2000) Subject Classification: 62 D05.
Sample Range ­ Some Stochastic Comparisons Results
Authors: Khaledi Baha-Eldin , Kochar Subhash
Published: August 2016

[Formula: see text]

AMS (2000) Subject classification: 60E15, 62N05, 62D05.
Hierarchical Bayesian Transition Models for the Analysis of Binary Longitudinal Data
Authors: Ghosh Malay , Maiti Tapabrata
Published: August 2016

The paper proposes a general hierarchical Bayesian methodology for the analysis of binary longitudinal data. The Bayesian method is implemented via Markov Chain Monte Carlo (MCMC) integration technique and is applied to a real dataset which was collected to study stereotyped behavior in deer mice.
Estimation in a Two-Stage Procedure for Failure Censored Model
Authors: Bandyopadhyay Uttam , Bhattacharya Rahul
Published: August 2016

A reliability setting is considered for comparing two competing equipments based on a fixed number of observations. A two stage failure censored design is proposed in which a preassigned number of items are randomised equally at the first stage and the better items are examined exclusively at the end of the second stage. Here at each stage, we consider type II censoring (see e.g. Miller (1981)) . That is, observations are made upto a common prefixed proportion of failures at each stage. For exponential responses, the exact bias and variance of the estimated failure rate difference at the end of the trial are derived. Competitors of the proposed procedure are also suggested. Some asymptotics related to all these procedures are also obtained.
The Asymptotic Distribution of Ln, K Test Statistic for Analyzing Nonreplicated Factorial Experiments
Authors: Al-Shiha A. A. , Yang S. S.
Published: August 2016

The asymptotic distribution of the test statistic proposed by Al-Shiha and Yang (1999) for analyzing nonreplicated factorials is deril- ed for large sample sizes. An extensive study is presented to compare the asymptotic percentiles with the empirical percentiles of the test statistic.
On Two Types of Cyclic Generalisations of EGD/2n- 1 PBIB Designs and Intereffect Orthogonality
Authors: Adhikary Basudeb , Bandyopadhyay Sanjoy
Published: August 2016

The purpose of this paper is to suggest two classes of block designs having orthogonal factorial structure (O.F.S.)
Characterization of Probability Distributions Through Conditional Expectation of Function of Two Order Statistics
Authors: Khan A.H. , Athar Haseeb , Yaqub M.
Published: August 2016

A general class of distribution F( x) = ah( x) + b has been characterized by considering conditional moments of a function of two order statistics, conditioned on the pair of order statistics. Further, its important consequences are also discussed.
On The Admissibility of Pitman Type Estimator Under Linex Loss Function
Authors: Farsipour N. Sanjari
Published: August 2016

In this paper the estimation of a Location parameter with an asymmetric Linex loss function is discussed. The admissibility of best location-invariant estimator under Linex loss, which we refer to it as Pitmantype estimator, is proved.
Towards a Dynamical Systems Approach to Protein Sequence Structure
Authors: Mitra Chanchal K. , Sen Arusharka
Published: August 2016

We explore statistical independence and dynamical system structures in protein primary sequences, based on the Swiss-Prot database. Results of testing for independence vs. Markov dependence in each sequence are reported. As for the dynamical systems, we discuss the problems of formulating a suitable fractal dimension for discrete state-space and estimating the embedding dimension as well as the link function. Some descriptive statistics for the sequences are also given.
Some Recent Results on Asymptotic Expansions of Multivariate Test Statistics for Mean Vectors Under Nonnormality
Authors: Fujiksohi Yasunori
Published: August 2016

In this paper we review some recent results on asymptotic expansions of some multivariate test statistics for mean vectors under nonnormality. It is assumed that the samples are taken from a general distribution satisfying Cramér's condition. Some methods are discussed, through the derivation of asymptotic expansions of the distributions of Hotelling's T2-statistic, one-way MANOVA test statistics, and some test statistics for a multivariate linear hypothesis on regression coefficients. The results are restricted to the null distributions, but we shall see that the methods could be extended to the non-null case. Relating to the methods, asymptotic expansions are given for the distributions of the sample mean vector, the sample covariance matrix, and multivariate t-statistics. We also give some results on robustness of the test statistics for departures from normality.
Recent Advances in Industrial Experimentations
Authors: Lin Dennis K.J.
Published: August 2016

Statistical experimental design has played an important role in industrial investigations. In this paper, we first discuss the major differences between running industrial and agricultural experiments. Thus, classical statistical experimental designs which are suitable for agricultural experimentation may not be appropriate for industrial experimentation. Some recent research, specifically for designing industrial experimentations, are then introduced. This includes computer experiment, impact of the dispersion effect in unreplicated fractional factorial design and optimal foldover plans.
A Weak Law with Random Indices for Randomly Weighted Sums of Rowwise Independent Random Elements in Rademacher Type p Banach Spaces
Authors: Rosalsky Andrew , Sreehari M. , Volodin Andrei I.
Published: August 2016

[Formula: see text]
Rates of Convergence of Estimated Change Points with Applications in Reliability
Authors: Herberts Tina , Jensen Uwe
Published: August 2016

We consider two models in reliability which deal with a change of the characteristics of a point process, namely a burn-in and a detection problem. Given a certain valuation structure both models lead to an optimization problem which can be viewed as an optimal stopping problem in continuous time. The solutions of these optimal stopping problems are derived by means of semimartingale representations of the underlying stochastic processes. The resulting optimal stopping times involve model parameters which are in general unknown. Using estimates of these model parameters leads to so-called estimated change points. It is investigated under which conditions and at which rate consistency of parameter estimates carries over to the corresponding sequence of estimated change points.
Bayesian Predictive Distribution with Right Invariant Priors
Authors: Komaki Fumiyasu
Published: August 2016

There exist many examples where Bayesian predictive distributions are more appropriate than plug-in distributions. When we use Bayesian procedure, the choice of prior distributions is a serious problem. Non-informative prior distributions or vague prior distributions are often adopted to construct Bayesian predictive distributions.

There exist many studies on the relation between priors and Bayes estimators. Here, we investigate the corresponding relation between priors and Bayesian predictive distributions. We adopt Kullback-Leibler divergence from the true distribution to a predictive distribution as a loss function .

We consider invariant predictive distributions. When a model has a group structure, the right invariant measure is often recommended as a noninformative prior. It is shown that Bayesian predictive distributions based on right invariant measures are the best invariant predictive distributions. We touch on shrinkage method of constructing predictive distributions.
Analyzying Bivariate Ordinal Polytomous Data: A Marginal Multinomial Logistic Approach
Authors: Das Kalyan , Sutradhar Brajendra C.
Published: August 2016

The multinomial cell counts based likelihood and the generalized estimating equations (GEE) approaches are widely used for analysis of bivariate ordinal categorical responses. In both of these approaches, the joint cell probabilities are usually modeled in terms of a global odds ratio as a measure of association and the marginal probabilities for each of the two ordered response variables. These methods utilize the stochastic ordering of the responses by modelling the cumulative margins with certain suitable link functions so that the link function of a cumulative margin is linear in covariates and an intercept representing the ordinal category. This type of modelling, therefore, requires suitable order restricted inference for the cutpoints (intercepts) separating the ordinal categories. These cutpoints are, however, frequently estimated in traditional ways without challenging their order restrictions. In this paper, we distinguish the ordinal categories in a general way so that the covariate effects are generally different under different ordinal categories. This allows one to model the cumulative margins through certain non-linear regression functions which does not require any introduction of the cutpoints.
On the Geometry of Censored Models
Authors: Marriott Paul , West Samantha
Published: August 2016

This paper looks at the process of censoring via the differential geometric theory of Amari (1990) . This theory gives both a conceptual framework and a set of useful tools which help in mastering the asymptotic theory of estimation and testing. After briefly reviewing results from the theory, noting the natural geometry enjoyed by exponential and curved exponential families, the paper examines how censoring can be viewed in a geometric way. In particular the issue of information loss and the sampling properties of estimators are examined. Throughout a visual approach is taken in order to aid intuition and to give insight into the geometric theory
Split Block Designs
Authors: Shah Kirti
Published: August 2016

Split block designs were introduced by Ozawa et al (2000) who established the optimality of the balanced split block designs for the estimation of the interaction effect. Here, we establish the same separately for each of the four strata and under fewer restrictions on the class of competing designs. Further, we give procedures for combined estimation and illustrate these for the balanced split block designs.
Optimum Stratification: A Mathematical Programming Approach
Authors: Khan E. A. , Khan M.G.M. , Ahsan M. J.
Published: August 2016

The probelm of determining the optimum strata boundaries, when the main study variable is used as stratification variable and a stratified sample, using Neyman allocation (for a fixed total sample size) is to be selected to estimate the population mean (or total), is formulated as a mathematical programming problem (MPP). It has been shown that with some modification this MPP may be converted into a multistage decision problem that could be solved using dynamic programming technique. Two numerial examples are also presnted to illustrate the computational details.
Variance Estimation by Jackknifing Method: A New Approach with Reference to Varying Probability Sampling
Authors: Roy Debesh , Safiquzzaman Md.
Published: August 2016

A new method of jackknifing has been suggested to take care of the imbalance in the sample, caused by varying probability of selection or by the distance of different data points from a central value of the sample.
A Unified Method to Sum a Variety of Infinite Series, with Applications
Authors: Dasgupta Anirban
Published: August 2016

Finding closed form formulas for sums of infinite series is of use and interest in many disciplines. Standard methods often involve special tricks for special series. The purpose of this article is to present a unified method to sum a large variety of infinite series, including complicated iterated series. The unification comes through the use of two probabilistic identities, resulting in exact integral representations for the various series and hence a closed form formula. Due to the large variety of series, including iterated series, for which exact formulas are produced, the results may also have some reference and instructional value.
On a Normal Mean with Known Coefficient of Variation
Authors: Guo Huizhen , Pal Nabendu
Published: August 2016

This paper deals with estimation of θ when iid (independent and identically distributed) observations are available from a N( θ, cθ2) distribution where c > 0 is assumed to be known. Using the equivariance principle under the group of scale and direction transformations we first characterize the class of equivariant estimators of θ. We then investigate a few equivariant estimators, including the maximum likelihood estimator, in terms of standardized bias and standardized mean squared error.
Interval Estimation in Adaptive Allocations Using Point Estimates
Authors: Bandyopadhyay Uttam , Biswas Atanu
Published: August 2016

Adaptive designs are sometimes used in clihical trials with a goal to allocate a larger number of patients to the better treatment in course of the trial. In the present paper, under the assumption of homogeneous entering patients, an approach of interval estimation to the treatment difference is suggested. The existing approach is the conditional interval estimation which is design independent under the homogeneity of patients. But here we suggest design dependent confidence intervals which is reasonably different under different adaptive designs. For the purpose of illustration we consider three adaptive designs, one is the well known randomized play-the-winner rule, and two new allocation rules. We compare these adaptive designs with a deterministic allocation rule which can be interpreted as the pairwise allocation. Finally we have tried to illustrate the method for all the designs using some real life data set on bladder cancer, which may not have direct relevance with the present set up.
Environmental Assessment Based on Multiple Indicators
Authors: Filar Jerzy A. , Ross N. Phillip , Wu Ming-lu
Published: August 2016

Environmental assessment is key to any environmental policy and is now among the highest priorities in socioeconomic development around the world. The present paper focuses on the application of multiple criteria decision making (MCDM) techniques to assessing the effectiveness of U S environmental policies for the reduction of toxic releases. The entropy concept is employed to assign suitable weights to the environmental indicators to reflect their relative importance in the assessment process.
Estimation for Some Stochastic Partial Differential Equations Based on Discrete Observations II
Authors: Rao B. L. S. Prakasa
Published: August 2016

Stochastic partial differential equations (SPDE) are used for stochastic modelling, for instance, in the study of neuronal behaviour in neurophysiology and in building stochastic models for turbulence. Huebner, Khasminskii and Rozovskii started the investigation of the maximum likelihood estiniatipn of the paramrters involved in two types of SPDE's and extended their results to a class of parabolic SPDE's. We obtained the Bernstein - von Mises type theorems for a class of parabolic SPDE's and investigated the properties of Bayes estimators of parameters involved in such SPDE's. In all the earlier works, it was assumed that a continuous observation of the random field uε( x, t) satisfying the SPDE over the region [0,' 1] x [0, T] is available. It is obvious that this assumption is not tenable in practice and the problem of interest is to develop methods of estimation of parameters from the random field uε( x, t) observed at discrete times t and at discrete positions x or from the Fourier coefficients uiε ( t) opserved at discrete time iustants. We construct consistent and asymptotically normal estimators of the parameter based on the Fourier coefficients uiε ( t)observed at discrete times tj = jδ, 0 ≤ j ≤ n where δ > 0 and n tends to infinity.
Improved Estimation of Regression Parameters in Measurement Error Models
Authors: Kim H. M. , Saleh A. K. MD. E.
Published: August 2016

This paper deals with improved estimation of the regrssion parameters in measurement error models when the reliability ratio matrix is known. We consider empirical Bayes estimators which include (i) the unrestricted unbiased (UE) estimator, (ii) the preliminary test estimator (PTE), (iii) the James-Stein estimator (SE), and (iv) the Positive-Rule Stein estimator (PRSE). The biases and the risks under the squared loss function are evaluated for all the four estimaton; and compared.
Choosing a Better Training Sample for Classifying an Individual into One of Two Correlated Normal Populations
Authors: Bandyopadhyay Subhadip , Bandyopadhyay Shibdas
Published: August 2016

The problem is to classify a unit into one of two populations which jointly constitute a bivariate normal population N2 ( μ1 , μ2, σ 2, σ 2, ρ]. Unlike the usual situation, the populations are not independent but correlated . A matched training sample consists of paired observations only. Earlier studies on classification in correlated setup considered the use of either matched training sample or independent training sample (set of only un-paired observations from each of the two populations). We consider classification problem in correlated setup hased on unbalanced training sample consisting of paired observations as well as single observations from each population. It is observed that probability of correct classification (PCC) of maximum likelihood (ML) rule based on unbalanced training sample is always higher than the minimum of the PCCs based on matched and independent training samples. Moreover, in some cases, it is maxiwnm among the three.
Tests for Reversed Hazard Rate Function
Authors: Nanda Asok K. , Paul Prasanta
Published: August 2016

The reversed hazard rate Junction of a random variable, defined as tlw ratio of the density to its distribution function, plays an important role in analyzing left-censored data. In this paper we develop tests based on the empirical distribution function for an assigned reversed hazard rate function against a onesided alternative and two different tests for equality of two reversed hazard rate functions. The asymptotic normality of the proposed test statistics has been established.
On the Geometric Mittag-Leffler Distributions
Authors: Jayakumar K. , Ajitha B.K.
Published: August 2016

As a generalization of geometric exponential distribution, geometric Mittag-Leffler distribution is studied. It is shown that the geometric Mittag- Leffler is the limit of geometric sums of Quasi Factorial gamma random variables. It can he seen that the geometric Mittag-Leffier distribution is geometrically infinitely divisible. As a generalization of the geometric Mittag-Leffler distribution, geometric Quasi Factorial gamma distributions are introduced and studied. It is shown that geometric sum of geometric Mittag-Leffler has geometric Quasi Factorial gamma distribution. Autoregressive process with geometric Mittag-Leffler margiuals are introduced and studied. Generalization to higher order autoregressive process is also done. A new class of discrete distributions related to discrete Mittag-Leffler laws, namely discrete geometric Mittag-Leffler distribution is introduced and its properties are studied.
Some Characterizations of a Pareto Distribution by Generalized Order Statistics
Authors: Samuel Philip
Published: August 2016

In this paper, some characterizations of Pareto distribution of the first kind using generalized order statistics are presented. These results are the generalization of the characterization results of the Pareto distribution based on order statistics as derived by Moothathu (1981).
α - Poisson Distribution
Authors: V. R. Saji Kumar
Published: August 2016

A characterization of α– Poisson distribution is obtained interms of a differential–difference equation of its probability density function.
Determining Gene­Environment Interaction Using Projected Score Method
Authors: Sinha Samiran
Published: August 2016

The present article proposes a new method for estimating multiplicative interactions between genetic and environmental factor on the risk of a dbease using projected score approach (Waterman and Lindsay {1996a, b)). First we review the existing methods for determining gene­environment interactions through case­control study and case­only study design. Then we discuss the proposed method based on projection theory. We derive an unbiased estimating equation for estimating the parameter of interest and then derive its asymptotic standard error. In addition, we derive a score statistic based on the derived estimating equation. The advantage of using the proposed method are : 1. Gain in efficiency of the parameter estimate and 2. Robustness to the other model parameters and gene­environment independence assumption. We apply the proposed method to a real case­control data on lung cancer. Finally, we compare the existing methods with the proposed method through a small simulation study which shows that the proposed method performs better than the existing methods in terms of efficiency in all situations irrespective of whether the genetic and environmental factor are independent in the population.
Classification Based on Multivariate Repeated Measures with Time Effect on Mean Vector and an AR (1) Correlation Structure on the Repeated Measures
Authors: Roy Anuradba , Khattree Ravindra
Published: August 2016

In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.