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Author: Deng-Yuan Huang Publisher: ISBN: Category : Languages : en Pages : 18
Book Description
The goal is to select from pi sub 1, ..., pi sub k (experimental treatments) those populations, if any, that are better (suitably defined) than pi sub 0 which is the control population. A locally optimal rule is derived in the class of rules for which Pr(pi sub i is selected) = gamma sub i, 1 = 1, ..., k, when theta sub 0 = theta sub 1 = ... = theta sub k. The criterion used for local optimality amounts to maximizing the efficiency in a certain sense of the rule in picking out the superior populations for specific configurations of theta = (theta sub 0, ..., theta sub k) in a neighborhood of an equiparameter configuration. The general result is then applied to the following special cases: (a) normal means comparison - common known variance, (b) normal means comparison - common unknown variance, (c) gamma scale parameters comparison - known (unequal) shape parameters, and (d) comparison of regression slopes. In all these cases, the rule is obtained based on samples of unequal sizes.
Author: Deng-Yuan Huang Publisher: ISBN: Category : Languages : en Pages : 18
Book Description
The goal is to select from pi sub 1, ..., pi sub k (experimental treatments) those populations, if any, that are better (suitably defined) than pi sub 0 which is the control population. A locally optimal rule is derived in the class of rules for which Pr(pi sub i is selected) = gamma sub i, 1 = 1, ..., k, when theta sub 0 = theta sub 1 = ... = theta sub k. The criterion used for local optimality amounts to maximizing the efficiency in a certain sense of the rule in picking out the superior populations for specific configurations of theta = (theta sub 0, ..., theta sub k) in a neighborhood of an equiparameter configuration. The general result is then applied to the following special cases: (a) normal means comparison - common known variance, (b) normal means comparison - common unknown variance, (c) gamma scale parameters comparison - known (unequal) shape parameters, and (d) comparison of regression slopes. In all these cases, the rule is obtained based on samples of unequal sizes.
Author: Deng-Yuan Huang Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
Let pi(o), pi(1), ..., pi(k) be k = 1 independent populations where pi(i) has the associated density function f(x, theta sub i) with the unknown parameter belonging to an interval H of the real line. Two types of problems are studied: (1) to select from pi(1), ..., pi(k) those populations, if any, that are better (to be suitably defined) than pi(o) which is the control population; and (2) to select from pi(1), ..., pi(k) a subset preferably of small size so as to contain the best population. For both problems, some locally optimal selection rules are derived. The optimality criteria employed in the two problems are different. Further, the procedure for the second problem is based on ranks though the densities are assumed to be known but for the values of the parameters. The rule in the first case is applied to the special cases of (1) normal means comparison with common known variance and unequal sample sizes; (2) normal means comparison with common unknown variance and unequal sample sizes, and (3) gamma scale parameters comparison with unequal shape parameters. The rank procedure is specialized to the case of logistic distributions. (Author).
Author: N. Balakrishnan Publisher: Springer Science & Business Media ISBN: 0817644229 Category : Mathematics Languages : en Pages : 439
Book Description
S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan’s influence and impact on these areas. Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.
Author: F. Liese Publisher: Springer Science & Business Media ISBN: 0387731946 Category : Mathematics Languages : en Pages : 696
Book Description
For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.
Author: S. S. Gupta Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
This paper deals with the derivation of subset selection rules which satisfy the basic P-condition and which locally maximize the probability of a correct selection among all invariant subset selection rules based on the ranks under the joint type II censoring. Following the earlier setup of Gupta, Huang and Nagel (1979), a locally optimal subset selection rule R1 is derived. The property of local monotonicity related to the rule R1 is discussed.
Author: Deng-Yuan Huang
Author: Deng-Yuan Huang
Author: Deng-Yuan Huang
Author: N. Balakrishnan
Author: F. Liese
Author: S. S. Gupta
Author: 
Author: North-Holland Publishing Company
Author: T. Liang
Author: S. S. Gupta
Author: