# Showing papers in "Calcutta Statistical Association Bulletin in 1980"

••

[...]

TL;DR: In this article, the concepts of intcr-effect-orthogonality and regularity in factorial experiments have been generalised to the concept of inter effect-ortho-onality of order t. and corresponding necessary and sufficient conditions have been given.

Abstract: The concepts of intcr-effect-orthogonality and regularity in factorial experiments as introduced by Mukerjee (1979) have been generalised to the concepts of inter-effect-orthogonality and regularity of order t. and corresponding necessary and sufficient conditions have been given. The problems of balancing, retaining full information and calculation of sums of squares have also been considered.

19 citations

••

[...]

TL;DR: In this paper, a method of construction of asymptotically minimal tolerance sets based on uniformly consistent density estimates is developed and application of the method in both parametric and nonparametric situations based on parameter estimates and window estimates of the density is considered.

Abstract: Multivariate β-content tolerance sets with asymptotic confidence level γ(0<γ⩽1) are defined and the requirement of asymptotic minimality for such sets is formulated. A method of construction of asymptotically minimal tolerance sets baFed on uniformly consistent density estimates ia developed. Application of the method in certain parametric situations based on parameter estimates and certain nonparametric situations based on window estimates of the density is considered.

16 citations

••

[...]

TL;DR: Asymptotic normality as well as some weak invariance principles for bonus sums and waiting times in an extended coupon collector's problem are considered and incorporated in the study of the asymptotics distribution theory of estimators of (finite) population totals in successive sub-sampling (or multistage sampling) with varying probabilities (without replacement) as mentioned in this paper.

Abstract: Asymptotic normality as well as some weak invariance principles for bonus sums and waiting times in an extended coupon collector's problem are considered and incorporated in the study of the asymptotic distribution theory of estimators of (finite) population totals in successive sub-sampling (or multistage sampling) with varying probabilities (without replacement). Some applications of these theorems are also considered.

10 citations

••

[...]

TL;DR: In this paper, it was shown that the proportional frequency criterion for orthogonal fractional factorial plans is not generally true and the criterion of equal frequency was established as a necessary and sufficient condition in the general case.

Abstract: This paper shows that the criterion of proportional frequency for (unblocked) orthogonal fractional factorial plans, as suggested by some previous authors, is not generally true. On the other hand, the criterion of equal frequency has been established as a necessary and sufficient condition in the general case. Some other properties of orthogonal fractional factorial plans have been investigated. A necessary and sufficient condition for designs involving two or more blocks has also been presented. A broad class of non-existence results follow.

8 citations

••

[...]

TL;DR: A new approach in assigning the treatments using multivariate methods is described, which is likely to be influenced by various prognostic factors and also on some or all interactions between the prognostic Factors if the interactions are present.

Abstract: In controlled clinical trials, the treatments are likely to be influenced by various prognostic factors, and while assigning treatments sequentially to the patients it is desirable to allot the treatments in such a way that the treatments are balanced over the main effects of prognostic factors and also on some or all interactions between the prognostic factors if the interactions are present. Efran (1971), Pocock and Simon (1975) and Freedman and White (1976) described some methods of balancing the treatments over the prognostic factors. In this paper, we shall describe a new approach in assigning the treatments using multivariate methods.

8 citations

••

[...]

TL;DR: In this article, it was shown that the conditional argument given in support of this was not correct, and hence, Theorem 3.1 holds, This can be seen as follows: it may be verified that {S n.m ; l <;n < r} where S n m is given by ( 3.4 ), is a martingale sequence uader 8 0 • Applying Theorem 2 of Brown (1971, p 60), it can be easily shown that under H 0, for fixed t,

Abstract: Io (3.10) (p 50, first line) of the paper, it was stated that hr.mEv+ in ~ the one-sided case <-win the two-sided case). But as with r tending to ao ,m also tends to infinity, the conditional argument given in support of this was not correct. However, the conclusion (3.10), and hence, Theorem 3.1 holds, This can be seen as follows. It may be verified that {S n .m ; l <;n < r} where S n .m is given by ( 3.4 ), is a martingale sequence uader 8 0 • Applying Theorem 2 of Brown (1971, p 60), it can be easily shown that, under H 0 , for fixed t,

7 citations

••

[...]

TL;DR: This paper has made an attempt to answer some of the problems of Hedayat and John (1974), which have many unsolved problems and in this process some related findings are presented.

Abstract: Hedayat and John (1974) opened up a new, elegant and practically useful area for research by introducing resistant and susceptible block designs. They have concluded their paper with many unsolved problems, which need to be attended. In this paper the author has made an attempt to answer some of those problems and in this process some related findings are also presented.

6 citations

••

[...]

TL;DR: In this paper, the authors improved upon Solliah's estimator and calculated the reduction in the risk when Σ is 2×2 and showed that it is better than the MLB of Σ.

Abstract: Abstract Solliah (1964), by considering the group of lower triangular matrices, suggested an estimator of the normal covariance matrix Σ when the mean vector is known and the loss function is tr ( Σ − 1 Σ ∧ − I ) 2 His estimator besides being minimax is better than the MLB of Σ. In this paper, we improve upon his estimator and calculate the reduction in the risk when Σ is 2×2.

6 citations

••

[...]

TL;DR: In this paper, the authors define a new notion of Pitman efficiency of sequential tests and examine in the light of this notion the asymptotic relative efficiencies of some sequential rank order tests with respect to the sequential probability ratio tests and sequential likelihood ratio tests.

Abstract: The paper defines a new notion of Pitman efficiency of sequential tests and examines in the light of this notion the asymptotic relative efficiencies of some sequential rank order tests with respect to the sequential probability ratio tests and sequential likelihood ratio tests.

5 citations

••

[...]

TL;DR: The definition of Partially Efficiency Balanced (PEB) designs is modified and it is shown that the PEB designs constitute the most general class which includes any conceivable design in the class of block designs.

Abstract: In this note we modify the definition of Partially Efficiency Balanced (PEB) designs as given by Puri et al (1977 a) and show that the PEB designs constitute the most general class which includes any conceivable design in the class of block designs.

••

[...]

TL;DR: In this paper, the symmetrized Des Raj estimator for a finite population total based on a PPSWOR sample of size two is shown to be admissible within (i) the class of all linear estimators and (ii) the classes of all unbiased estimators.

Abstract: The symmetrized Des Raj estimator for a finite population total based on a PPSWOR sample of size two is shown to be admissible within (i) the class of all linear estimators and (ii) the class of all unbiased estimators. In this connection we have obtained a class of admissible linear estimators of the population total which includes the sample mean multiplied by the population size and the classical ratio estimator for any arbitrary sampling design.

••

[...]

TL;DR: A randomised response technique for estimating the proportion of individuals in several unrelated (in some sense) ‘sensitive’ groups is suggested and is observed to fare well in some realistic situations.

Abstract: In survey sampling, problems often arise when respondents are asked sensitive questions or questions of highly personal nature. In such cases people often refuse to answer, or give false answers. In this paper we have suggested a randomised response technique for estimating the proportion of individuals in several unrelated (in some sense) ‘sensitive’ groups. The proposed model is observed to fare well in some realistic situations.

••

[...]

TL;DR: In this paper, Ghosh and Sinha have given a complete characterization of the design matrix for the robustness of the likelihood ratio test for linear hypotheses, and an alternative proof of the result which gives a better Insight into the problem.

Abstract: For the usual normal linear model with an lntraclass covariance structure, Ghosh and Sinha (1978) has given a complete characterization of tho design matrix for the robustness of the likelihood ratio test for linear hypotheses. We indicate here an alternative proof of the result which gives a better Insight into the problem.

••

[...]

TL;DR: The sample mean based on distinct units for k (⩾ 2) independent interpenetrating samples drawn according to SRSWOR is shown to be more (less) efficient than one based on a single SRSWR (SRSWOR) sample with the same expected effective size as mentioned in this paper.

Abstract: The sample mean based on distinct units for k (⩾ 2) independent interpenetrating samples drawn according to SRSWOR is shown to be more (less) efficient than one based on a single SRSWR (SRSWOR) sample with the same expected effective size.