Construction of orthogonal and nearly orthogonal Latin hypercubes (2009)
Lin, C. Devon, Mukerjee, Rahul, Tang, Boxin
We propose a method for constructing orthogonal or nearly orthogonal Latin hypercubes. The method yields a large Latin hypercube by coupling an orthogonal array of index unity with a small Latin...
Data-dependent probability matching priors for empirical and related likelihoods (2008)
We consider a general class of empirical-type likelihoods and develop higher order asymptotics with a view to characterizing members thereof that allow the existence of possibly data-dependent...
OPTIMAL (2, n) VISUAL CRYPTOGRAPHIC SCHEMES (2008)
Abstract: In (2, n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares which are distributed among n participants. The image cannot be decoded from any single...
Optimal factorial designs for cDNA microarray experiments (2008)
Banerjee, Tathagata, Mukerjee, Rahul
We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects...
: Considering general prime or prime powered factorials, we give a finite projective geometric formulation for regular fractional factorial splitplot designs. This provides a unified framework for...
Comparison Of Test Statistics Via Expected Lengths Of Associated Confidence Intervals (2007)
Rahul Mukerjee Indian, Rahul Mukerjee, Nancy Reid
With reference to a large class of test statistics, higher order asymptotics on expected lengths of associated confidence intervals are investigated in a possibly non-iid setting. The connection with...
On A Property Of Probability Matching Priors: Matching The Alternative Coverage Probabilities (2007)
this paper how far a prior satisfying (1.1) also matches P ` f` 1 +
A Conversation with Shoutir Kishore Chatterjee (2007)
Banerjee, Tathagata, Mukerjee, Rahul
Shoutir Kishore Chatterjee was born in Ranchi, a small hill station in India, on November 6, 1934. He received his B.Sc. in statistics from the Presidency College, Calcutta, in 1954, and M.Sc. and...
Fang, Kai-Tai, Mukerjee, Rahul
With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest...
Expected lengths of confidence intervals based on empirical discrepancy statistics (2005)
Fang, Kai-tai, Mukerjee, Rahul
We consider a very general class of empirical discrepancy statistics that includes the Cressie–Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order...
On an exact probability matching property of right-invariant priors (2002)
Severini, Thomas A., Mukerjee, Rahul, Ghosh, Malay
The paper considers priors which are right invariant with respect to the Haar measure. It is shown that the posterior coverage probabilities of certain invariant Bayesian predictive regions exactly...
Optimal main effect plans with non-orthogonal blocking (2002)
Mukerjee, Rahul, Dey, Aloke, Chatterjee, Kashinath
The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block...
Blocked regular fractional factorial designs with maximum estimation capacity (2001)
Cheng, Ching-Shui, Mukerjee, Rahul
In this paper, the problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to Fries and Hunter is a wellaccepted criterion...
Conditions are obtained for the approximate frequentist validity of the posterior quantiles of any smooth parametric function. An application to Bayesian tolerance limits is indicated.
Bayesian prediction with approximate frequentist validity (2000)
Datta, Gauri Sankar, Ghosh, Malay, Mukerjee, Rahul, Sweeting, Trevor J.
We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering...
Blocking in regular fractional factorials: a projective geometric approach (1999)
A projective geometric characterization is given of the existence of any regular main effect $s^{n-k}$ design in $s^{\gamma}$ blocks. It leads to a constructive method for finding a maximal blocking...
On the optimality of orthogonal array plus one run plans (1999)
Much contrary to popular belief and even a published result, it is seen that orthogonal array plus one run plans are not necessarily optimal, within the relevant class, for general $s_1 \times \dots...
Uniformity In Fractional Factorials (1999)
Kai-tai Fang, Chang-xing Ma, Rahul Mukerjee
. The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For...
On Confidence Intervals Associated with the Usual and Adjusted Likelihoods (1999)
: In the presence of nuisance parameters, we derive an explicit higher order asymptotic formula to compare the expected lengths of con#dence intervals given by likelihood ratio statistics arising...
Connection Between Uniformity and Aberration in Regular Fractions of Two-level Factorials (1999)
We show a link between two apparently unrelated areas, namely uniformity and minimum aberration, both of which have been of substantial recent interest. Specifically, with reference to regular...
On Confidence Intervals Associated with the Usual and Adjusted Likelihoods (1999)
: In the presence of nuisance parameters, we derive an explicit higher order asymptotic formula to compare the expected lengths of confidence intervals given by likelihood ratio statistics arising...
Regular fractional factorial designs with minimum aberration and maximum estimation capacity (1998)
Cheng, Ching-Shui, Mukerjee, Rahul
Using the approach of finite projective geometry, we make a systematic study of estimation capacity, a criterion of model robustness, under the absence of interactions involving three or more...
Optimal partial diallel crosses (1997)
Even in the absence of blocks, each cross in a partial diallel cross design can be formally identified with a ‘block’ of size two and thus the design itself can be identified with a binary block...
Second-order probability matching priors (1997)
The paper considers priors obtained by ensuring approximate frequentist validity of (a) posterior quantiles, and of (b) the posterior distribution function. It is seen that, at the second order of...
On the existence of saturated and nearly saturated asymmetrical orthogonal arrays (1995)
Mukerjee, Rahul, Wu, C. F. Jeff
We develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2. This condition limits the choice of integral solutions to the system of...
MUKERJEE, RAHUL, DEY, DIPAK K.
Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior...
Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox and Reid (1991)
MUKERJEE, RAHUL, CHANDRA, TAPAS K.
This paper explicitly derives a Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox & Reid via that for the usual likelihood ratio statistic.
Optimal estimation of a finite population mean in the presence of linear trend (1990)
Postulating different superpopulation models for a finite population with linear trend, we suggest optimal sampling strategies for estimating the finite population mean within some classes of...
Optimal estimation of finite population total under a general correlated model (1989)
Restricting attention to fixed size sampling designs and linear unbiased estimators of a finite population total, we give methods for finding estimators with minimum model expected variance and the...
Optimal design for the estimation of variance components (1988)
The design problem for the estimation of variance components by the method of unweighted squares of means, under a multifactor random effects model, is considered. First it is shown that with the...
On resolvable and affine resolvable variance-balanced designs (1985)
MUKERJEE, RAHUL, KAGEYAMA, SANPEI
This paper introduces the notion of affine (μ1, …, μ1)-resolvability and explores the interrelations between: (a) affine (μ1…, μ1)-resolvability, (b) variance-balance, and (c) the relation b...
Minimax second- and third-order designs to estimate the slope of a response surface (1985)
Designs for estimating the slope of a response surface are considered. Minimization of the variance of the estimated slope maximized over all points in the factor space is taken as the optimality...
Minimizing the maximum variance of the difference between two estimated responses (1984)
Minimization of the variance of the difference between estimated responses at two points maximized over all pairs of points in the design space is taken as the criterion for selecting designs....
On Expected Lengths of Predictive Intervals
We consider the problem of comparing predictive intervals for a future observation via their expected lengths at a given confidence level. A higher order asymptotic theory is developed. This...
Optimal main effect plans with non-orthogonal blocking
The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block...
Expected lengths of confidence intervals based on empirical discrepancy statistics
We consider a very general class of empirical discrepancy statistics that includes the Cressie--Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order...
With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest...
Bayesian and frequentist confidence intervals arising from empirical-type likelihoods
For a general class of empirical-type likelihoods for the population mean, higher-order asymptotics are developed with a view to characterizing its members which allow, for any given prior, the...
Optimality of balanced designs for minimum norm quadratic unbiased estimation of variance components
Approximate theory, balanced design, one-way data, optimality,
Almost saturatedD-optimal main effect plans and allied results
62K15, 62K05, A-efficiency, D-optimality, unimodular matrix,
On the Positive Definiteness of the Information Matrix Under the Binary and Poisson Mixed Models
Rahul Mukerjee, Brajendra Sutradhar
Estimating function, Fisher information matrix, generalised linear mixed model, joint estimates, likelihood estimation, positive definiteness, regression effects, variance component of the random...
Efficiency of connected binary block designs when a single observation is unavailable
Subir Ghosh, Sanpei Kageyama, Rahul Mukerjee
Balanced incomplete block design, connectedness, efficiency, group divisible design, robustness,
Kronecker factorial designs for multiway elimination of heterogeneity
Efficiency, Kronecker product, orthogonal array, orthogonal factorial structure, projection,
An extension of the conditional likelihood ratio test to the general multiparameter case
Adjusted likelihood, conditional likelihood, contiguous alternative, local maximinity, parametric orthogonality, power, second order,
Frequentist validity of highest posterior density regions in the multiparameter case
Highest posterior density, Jeffreys' prior, non-informative prior, parametric orthogonality,
Average power, Bartlett-type adjustment, Confidence interval, Contiguous alternatives, Edgeworth expansion, Empirical likelihood, Minimaxity, Second-order, Third-order,
Bayesian prediction, frequentist validity, highest predictive density region, noninformative prior, posterior quantile, regression, shrinkage argument,
Comparison of LR, Score, and Wald Tests in a Non-IID Setting
Rao, C. Radhakrishna, Mukerjee, Rahul
Considering a large class of tests, we study higher order power in a possibly non-iid set-up. Optimum properties for the likelihood ratio and score tests are exhibited under the criteria of...
Ghosh, Jayanta K., Mukerjee, Rahul, Sen, Pranab K.
In a multiparameter estimation problem, for first-order efficient estimators, second-order Pitman admissibility, and Pitman closeness properties are studied. Bearing in mind the dominant role of...
In a multiparameter situation, this paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio statistic differ by o(1). The role of Jeffreys'...
Bartlett-type modification for Rao's efficient score statistic
Chandra, Tapas K., Mukerjee, Rahul
This paper suggests simple Bartlett-type modifications for a wide class of test statistics that includes in particular the efficient score and the likelihood ratio statistics.
Comparison of tests in the multiparameter case I. Second-order power
In a multiparameter setting, considering a very large class of tests it is seen that under contiguous alternatives, unlike in the one-parameter case, identity of power up to the first order may not...
Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test
In a general multiparameter setup, this paper proves an optimality property of Rao's test, in terms of maximization of "average" third-order power under contiguous alternatives, within a very wide...
Comparison between the locally most powerful unbiased and Rao's tests
Mukerjee, Rahul, Chandra, Tapas K.
Consider the problem of testing a simple hypothesis that [theta] = 0 against the alternative that [theta] [not equal to] 0. This paper makes an asymptotic comparison (up to o(n-1)) between Rao's test...
Chang, In Hong, Mukerjee, Rahul
We consider a general class of empirical-type likelihoods for a vector-valued population mean. Members of the class that admit a matching prior, in a higher order asymptotic sense, for the posterior...
Probability matching property of adjusted likelihoods
Chang, In Hong, Mukerjee, Rahul
For models characterized by a scalar parameter, it is well known that Jeffrey's prior ensures approximate frequentist validity of posterior quantiles. We examine how far this result remains robust in...
Asymptotic results on the frequentist mean squared error of generalized Bayes point predictors
Chang, In Hong, Mukerjee, Rahul
An asymptotic formula for the frequentist mean squared error (MSE) of generalized Bayes point predictors is worked out. This formula yields an explicit second-order admissibility result when the...
Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics
Basu, Ruma, Ghosh, J. K., Mukerjee, Rahul
We explore two proposals for finding empirical Bayes prediction intervals under a normal regression model. The coverage probabilities and expected lengths of such intervals are studied and compared...
Chang, In Hong, Kim, Byung Hwee, Mukerjee, Rahul
We characterize priors that ensure approximate frequentist validity of posterior quantiles of unobservable random effects. Application to analysis of variance (ANOVA) models is explored.
A characterization for orthogonal arrays of strength two via a regression model
Chan, Ling-Yau, Fang, Kai-Tai, Mukerjee, Rahul
We give a characterization for orthogonal arrays of strength two in terms of D-optimality under a multiple regression model with continuous factor levels.
A simple Bartlett-type modification has been obtained for Rao's efficient score statistic in the presence of a nuisance parameter. The use of parametric orthogonality has been helpful in the...
Fourth-order rotatable designs: A-optimal measures
The A-optimal rotatable design measures are derived for fourth-order polynomial regression on hyperspheres. The application of the association algebra of triangular association scheme is helpful in...
Universal optimality of main effect deletion designs
Mukerjee, Rahul, Gupta, Sudhir
The universal optimality of certain deletion designs with respect to main effects has been proved. In particular, this settles a recent conjecture by Voss (1986).
Minimax second-order designs for difference between estimated responses in extrapolation region
Minimization of the variance of the difference between estimated response at two response at two points maximized over all pairs of points in the extrapolation region is taken as the criterion for...
Characterization of normality within the class of elliptical contoured distributions
Khatri, C. G., Mukerjee, Rahul
The random vector x is said to have an elliptical contoured distribution provided its characteristic function (c.f.) is exp([radical sign]- 1 t'[mu]) [phi] (t' [Sigma]t) for all t [epsilon] Rp, where...
Edgeworth expansion, Higher order asymptotics, Posterior coverage, 62F15, 62F25,