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Full Product Details

Author:   BÜRINGER ,  MARTIN ,  SCHRIEVER ,  Buringer
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   Softcover reprint of the original 1st ed. 1980
Dimensions:   Width: 15.20cm , Height: 2.60cm , Length: 22.90cm
Weight:   0.785kg
ISBN:  

9780817630218

ISBN 10:   081763021
Pages:   489
Publication Date:   01 January 1980
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

General Introduction.- 1 Sequential Procedures for Selecting the Best of k ? 2 Binomial Populations Introduction.- 1 Selection Procedures with Unrestricted Patient Horizon.- 1 The Selection Model [2; PW; |SA?SB| = r].- 1.1 Derivation of the critical r-value.- 1.2 Derivation of the expectations.- 2 The Selection Model [2; VT; |SA?SB| = s].- 2.1 Derivation of the critical s-value.- 2.2 Derivation of the expectations.- 3 The Selection Model [2; PL; |FA?FB| = r].- 3.1 Derivation of the critical r-value.- 3.2 Derivation of the expectations.- 4 Comparison of the Selection Procedures No.1-No..- 4.1 Some general remarks.- 4.2 Comparison of PW- and VT-sampling.- 4.3 Comparison of PW- and PL-sampling.- 4.4 Comparison of PL- and VT-sampling.- 4.5 Recapitulation.- 4.6 Concluding remarks.- 4.7 Numerical results.- 5 Two-Stage Selection Procedures.- 5.1 The structure of two-stage selection procedures.- 5.2 Derivation of P(CS).- 5.3 Derivation of s(m,n,kc,M) and r(m,n,kc,M).- 5.4 Derivation of the expectations.- 5.5 Addition of PL-sampling.- 5.6 Concluding remarks.- 5.7 Numerical results.- 6 The Selection Model [2; PW; max{SA,SB} = r].- 6.1 Derivation of the critical r-value.- 6.2 Derivation of the expectations.- 6.3 Expectations for large r.- 7 The Selection Model [2; VT; max{SA,SB} = r].- 7.1 Derivation of the critical r-value.- 7.2 Derivation of the expectations.- 7.3 Expectations for large r.- 8 Comparison of the Selection Models No.6 and No.7 - Some Modifications of these Models.- 8.1 Comparison of the selection models no.6 and no.7.- 8.2 The selection model [2; PW; min{FA,FB} = r].- 8.3 The selection model [2; PL; max{FA,FB} = r].- 8.4 Concluding remarks.- 8.5 Numerical results.- 9 The Nature of Termination of a Classical Sequential Selection Procedure.- 9.1 Basic notions.- 9.2 The stopping-behaviour of selection model no.1.- 9.3 The stopping-behaviour of selection model no.2.- 9.4 The stopping-behaviour of the selection models no.3 and no.5.- 9.5 The stopping-behaviour of selection model no.6.- 9.6 The stopping-behaviour of selection model no.7.- 10 The Selection Model [k; PW; max{S1,...,Sk} = r].- 10.1 Introductory remarks.- 10.2 Derivation of the critical r-value.- 10.3 Derivation of the expectations.- 10.4 Expectations for large r.- 11 The Selection Model [k; VT; max{S1,...,Sk} = r].- 11.1 Derivation of the critical r-value.- 11.2 Derivation of the expectations.- 11.3 Expectations for large r.- 11.4 Concluding remarks.- 11.5 Numerical results.- 12 Expected Truncation Points.- 13 The Selection Model [2;PW;|SA-SB|=r or $$\left| {{{\hat p}_A} - {{\hat p}_B}} \right| \geqslant c/\left( {{F_A} + {F_B}} \right)$$].- 13.1 Introduction.- 13.2 Derivation of the critical r- and c-values.- 13.3 Numerical results.- 14 The Selection Model [2;VT;|SA-SB|=s or $$\left| {{{\hat p}_A} - {{\hat p}_B}} \right| \geqslant d/\left( {{F_A} + {F_B}} \right)$$].- 14.1 Derivation of the critical s- and d-values.- 14.2 Numerical results.- 15 The Selection Models [k;PW;el.Ai if Sj?Si=r] and [k;VT;e1.Ai if Sj?Si=s].- 15.1 The PW-elimination procedure.- 15.2 The VT-elimination procedure.- 15.3 Numerical results for the PW-procedure.- 15.4 Numerical results for the VT-procedure.- 15.5 Comparison of selection models.- 2 Selection Procedures with Restricted Patient Horizon.- 1 The Selection Model [2; PW; max{SA+FB, SB+FA} = r].- 1.1 Introduction.- 1.2 Derivation of the P (CS)-value.- 1.3 Determination of the LFC.- 1.4 Derivation of the critical r-value.- 1.5 Derivation of the expectations.- 1.6 Numerical results.- 2 The Selection Model [2; PW; max{SA,SB} = r or FA=FB = c].- 2.1 Derivation of the P (CS)-value.- 2.2 Derivation of the critical r- and c-values.- 2.3 Derivation of the expectations.- 2.4 Numerical results.- 3 The Selection Model [2; VT; max{SA,SB} = r or min{FA,FB} = c].- 3.1 Derivation of the P (CS)-value.- 3.2 Derivation of the critical r- and c-values.- 3.3 Derivation of the expectations.- 3.4 Numerical results.- 4 The Selection Model [2; VT; max{SA,SB} = r or max{FA,FB} = c].- 4.1 Derivation of the P (CS)-value.- 4.2 Derivation of the critical r- and c-values.- 4.3 Derivation of the expectations.- 4.4 Numerical results.- 5 The Selection Model [2; PW; |SA?SB| = r or FA+FB = s].- 5.1 Derivation of the P (CS)-value.- 5.2 Derivation of the critical r- and s-values.- 5.3 Derivation of the expectations.- 5.4 Numerical results.- 6 The Selection Model [k;PW;max{S1,...,Sk}=r or min{F1,...,Fk}=c].- 6.1 Introductory remarks.- 6.2 Derivation of the P (CS)-value.- 6.3 Derivation of the critical r- and c-values.- 6.4 Derivation of the expectations.- 6.5 Numerical results.- 7 The Selection Model [k;VT;max{S1,...,Sk}=r or min{F1,...,Fk}=c].- 7.1 Derivation of the P (CS)-value.- 7.2 Derivation of the critical r- and c-values.- 7.3 Derivation of the expectations.- 7.4 Numerical results.- 8 The Selection Model [k;VT;max{S1,...,Sk}=r or el.Ai if Fi=c].- 8.1 Derivation of the P (CS)-value.- 8.2 Derivation of the critical r- and c-values.- 8.3 Numerical results.- 9 Further Elimination Procedures.- 9.1 The selection model [k;PW;e1.Ai if Sj-Si=r or if Fi=c].- 9.2 The selection model (k;VT;el.Ai if Sj-Si=r or if Fi=c].- 9.3 The selection model [k;PW;e1.Ai if Sj-Si=r or stop if F1+...+Fk=s].- 9.4 The selection model [k;PW;el.Ai if Sj-Si=r or el.Ai if $${\hat p_j} - {\hat p_i} \geqslant c/\left( {{F_i} + {F_j}} \right)$$].- 9.5 The selection model [k;VT;el.Ai if Sj-Si=r or el.Ai if $${\hat p_j} - {\hat p_i} \geqslant d/\left( {{F_i} + {F_j}} \right)$$].- 9.6 Numerical results.- 9.7 Comparison of selection models.- 9.8 Further selection procedures.- 3 Selection Procedures with Fixed Patient Horizon.- 1 Historical Remarks.- 2 The Zelen Selection Model.- 2.1 Definition of the model.- 2.2 Comparison with a VT-sampling procedure.- 2.3 Determination of the optimal value of n.- 3 The Selection Models [2;PW;fixed N] and [2;VT;fixed N].- 3.1 Introduction.- 3.2 Comparison of the P (CS)-values.- 3.3 Comparison of the expectations.- 3.4 Exact and asymptotic formulae for E (NB).- 3.5 Extension of the selection models to odd N.- 3.6 Numerical results.- 3.7 Equivalence to Hoel's selection model.- 4 The Selection Models [2;PW;fixed N] and [2;VT;fixed N] with Curtailment.- 4.1 Introductory remarks.- 4.2 The PW-sampling procedure with curtailment.- 4.3 The VT-sampling procedure with curtailment.- 4.4 Numerical results.- 5 The Selection Model [2;VT;fixed N] with Truncation Based on |SA?SB|.- 5.1 Description of the model.- 5.2 Derivation of the P (CS)-value.- 5.3 Derivation of the probability of declaring the two treatments equal.- 5.4 Derivation of an upper bound for E (NB).- 5.5 Derivation of the truncation points and of the patient horizon N.- 5.6 Numerical results.- 6 The Selection Model [2;PW;fixed N] with Truncation Based on |SA?SB|.- 6.1 Description of the model.- 6.2 Derivation of the P (CS)-value.- 6.3 Derivation of the probability of declaring the two treatments equal.- 6.4 Derivation of E (NB).- 6.5 Numerical results.- 6.6 Comparison of the selection models.- 7 Selection Models Based on the Randomized Play-the-Winner Rule.- 7.1 Introductory remarks.- 7.2 Expected number of patients on the better treatment within n trials.- 7.3 Derivation of the P(CS)-values.- 7.4 Derivation of the expectations.- 7.5 Numerical results.- 8 Supplementary Investigations-Topics Requiring Further Research.- 2 Continuous Response Selection Models Introduction.- 1 Subset-Selection Procedures Based on Linear Rank-Order Statistics.- 1 Linear Rank-Order Statistics and their Asymptotic Distributions.- 1.1 The general linear rank-order statistic.- 1.2 Some special linear rank-order statistics.- 1.3 The joint asymptotic distribution of the vector of rank-order statistics (S1,...,Sk) based on joint ranks.- 1.4 The treatment of ties.- 2 Two Subset-Selection Procedures in One-Factor-Designs Including the General Behrens-Fisher-Problem.- 2.1 The selection rule R1.- 2.2 The infimum of the probability P(CS | R1).- 2.3 The asymptotic distributions of two special rank-order statistics in case of consistent estimation of the unknown parameters.- 2.4 The probability P(CS | R1) in the LFC.- 2.5 A numerical example.- 2.6 Some Monte-Carlo studies.- 3 The Selection Rule R1 in the Case of Equal Scale-Parameters.- 3.1 The probability P(CS | R1) in the LFC.- 3.2 The Haga-statistic.- 3.3 A numerical example.- 3.4 Some Monte-Carlo studies.- 4 A Further Class of Subset-Selection Procedures in One-Factor Designs.- 4.1 The selection rule R2.- 4.2 The infimum of the probability P(CS | R2).- 4.3 Exact and asymptotic distribution of max Sj?S1 for identically distributed populations.- 4.4 A numerical example.- 4.5 Some Monte-Carlo studies.- 5 Some Properties of Optimality and a Brief Comparison of the Procedures No.2 - No.4.- 5.1 Local optimality of selection rule R1.- 5.2 Influence of the scorefunctions on the efficiency of procedures based on rules R1 and R2.- 5.3 Comparison of the procedures given in sections 2,3,and 4.- 6 The Selection Rules R1 and R2 in Case of Randomized-Block-Designs.- 6.1 Modified definition of ranks and the distribution of the resul-ting rank-order statistics.- 6.2 The rules R1 and R2.- 6.3 The asymptotic and the exact distribution of max Sl?S1 for identical parameters.- 6.4 A numerical example.- 6.5 Some Monte-Carlo studies.- 2 Asymptotic Distribution-Free Sequential Selection Procedures Based on an Indifference-Zone Model.- 1 Introduction.- 2 A Class of Estimators of the Functions fi(?1,...,?k).- 2.1 General one-sample rank-order statistics.- 2.2 The one-sample rank-order statistics based on median-scores.- 2.3 The general Hodges-Lehmann-estimator.- 2.4 A class of compatible estimators of the functions fi(?1,...,?k).- 3 Several Strongly Consistent Estimators.- 3.1 An estimator of (B2(G))-1.- 3.2 An estimator of (g(0)2)-1.- 3.3 Two estimators of ?j(G) and G*(0,0).- 4 A Class of Sequential Selection Procedures.- 4.1 Definition of the selection procedures.- 4.2 Some important properties of the sequential selection procedures.- 5 A Numerical Example and some Remarks Concerning the Practical Working with the Sequential Procedures.- 5.1 An example.- 5.2 The implementation of the procedures.- 6 Another Class of Sequential Selection Procedures.- 7 Asymptotic Efficiency and some Monte-Carlo Studies.- 7.1 The asymptotic efficiency of the procedures of section 4 with respect to the procedures of section 6.- 7.2 Some Monte-Carlo studies of the procedures given in section 4 and 6.- 7.3 Some remarks concerning the application of general scorefunctions.- 3 Methods for Selecting an Optimal Scorefunction.- 1 The Basic Idea.- 2 Two Statistics for Characterizing a Distribution.- 2.1 An estimator for the skewness of some distribution.- 2.2 An estimator for the peakedness of some distribution.- 3 Two Methods for Selecting a Scorefunction.- 3.1 Selection based on the joint sample.- 3.2 Selection based on the single samples.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- Appendix 5.- Appendix 6.- Abbreviations.- References.

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