Showing papers by "Rahul Mukerjee published in 2000"
TL;DR: In this paper, the centred L2-discrepancy measure for uniformity in terms of the word-length pattern has been shown to be related to minimum aberration.
Abstract: SUMMARY We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L2-discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.
123 citations
TL;DR: It is shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.
Abstract: 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 both posterior quantiles and highest predictive density regions with reference to a future observation The resulting priors are shown to be invariant under reparameterization The role of Jeffreys' prior in this regard is also investigated It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched
51 citations
TL;DR: In this paper, the equivalence of second order quantile matching priors and highest posterior density regions matching prior within the class of first-order quantile priors was established.
Abstract: The paper has three components. First, for a realvalued parameter of interest orthogonal (Cox and Reid, 1987) to the nuisance parameter vector, we find a necessary and sufficient condition for the equivalence of second order quantile matching priors and highest posterior density regions matching priors within the class of first order quantile matching priors. Examples are presented to illustrate the result. Second, we develop a quantile matching prior in a normal hierarchical Bayesian model. This prior turns out to be different from the one proposed earlier by Morris (1983). Third, we obtain an exact matching result when the objective is prediction of a real-valued random variable from a location family of distributions.AMS (2000) Subject Classification: 62F15, 62F25, 62E20
37 citations
01 Jan 2000
TL;DR: In this paper, a finite projective geometric approach was used to investigate the maximum estimation capacity in regular fractions of mixed factorials, recognizing the fact that not all two-factor interactions may have equal importance in such a set-up.
Abstract: We use a finite projective geometric approach to investigate the issue of maximum estimation capacity in regular fractions of mixed factorials, recognizing the fact that not all two-factor interactions may have equal importance in such a set-up. Our results provide further statistical justification for the popular criterion of minimum aberration as applied to mixed factorials.
3 citations
TL;DR: In this article, Ahmed et al. make it explicit that b xz in t 5 is an ordinary and not a partial regression coefficient, and they also make it clear that Tripathi & Ahmed's estimator t 0, quoted also in Ahmed (1998), is no better than t 5 of Mukerjee at al.
Abstract: In the estimators t 3 , t 4 , t 5 of Mukerjee, Rao & Vijayan (1987), b yx and b yz are partial regression coefficients of y on x and z, respectively, based on the smaller sample. With the above interpretation of b yx and b yz in t 3 , t 4 , t 5 , all the calculations in Mukerjee at al.(1987) are correct. In this connection, we also wish to make it explicit that b xz in t 5 is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t 3 , t 4 , t 5 , as given in Ahmed (1998 Section 3) are computed assuming that our b yx and b yz are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t 0 , quoted also in Ahmed (1998), is no better than t 5 of Mukerjee at al.(1987).