Developments in Statistics

¿List of ContributorsPrefaceContents of Volume 1Chapter 1 Random Vibration of One- and Two-Dimensional Structures I. Introduction A. Description of the Problem B. Statistical Terminology II. One-Dimensional Structures A. Formal Analysis for Stationary Response B. Approximate Solutions Based on Modal Sums C. Approximate Solutions Based on Image Sums III. Two-Dimensional Structures A. Formal Analysis for Stationary Response B. Approximate Solutions Based on Modal Sums C. Approximate Solutions Based on Image Sums D. Experimental Techniques ReferencesChapter 2 The Statistical Theory of Linear Systems 1. Introduction 2. The Structure of Linear Systems with Rational Transfer Functions 3. The Asymptotic Properties of ML Estimates 4. The Construction of Estimates of the Parameters 5. Recursive Methods 6. Some Further Problems ReferencesChapter 3 Bispectra and Energy Transfer in Grid-Generated Turbulence 1. Introduction 2. Bispectra and Energy Transfer 3. Symmetry Conditions and Isotropy 4. Experimental Arrangements 5. Analysis of Hot-Wire Calibration 6. Computational Method 7. Computational Symmetries 8. Bispectra and One-Dimensional Energy Transfer 9. Experimental Results 9.1. Moments and Second-Order Spectra 9.2. Bispectra 9.3. One-Dimensional Energy Transfer Spectra 10. Concluding Remarks ReferencesChapter 4 Some Developments on Simultaneous Test Procedures 1. Introduction 2. Multivariate t, Multivariate F, and Multivariate Gamma Distributions 3. Distributions of Correlated Quadratic Forms and Related Distributions 4. Finite Intersection Tests for Multiple Comparisons of Means 5. Finite Intersection Tests and Step-Down Procedure for Multiple Comparisons of Mean Vectors 6. Largest Root Test and T2max Test 7. Simultaneous Tests under Regression Models 8. Simultaneous Tests under Polynomial Growth Curve Models When Errors Are Autocorrelated 9. Multiple Comparisons of Means of Correlated Normal Populations 10. Multiple Comparisons of Variances of Correlated Normal Populations 11. Simultaneous Tests under Growth Curve Models 12. Simultaneous Tests for the Equality of the Covariance Matrices of Multivariate Normal Populations 13. Simultaneous Tests When Covariance Matrices Have Special Structures 14. Tests for the Structure of Interaction under Two-Way Classification Model 15. Selection of Populations ReferencesChapter 5 Stochastic Markovian Fields 1. Splitting Subspaces 2. Markovian Sets 3. Dual Stochastic Fields and Markov Property 4. Linear Stochastic Equations 5. Stationary Fields ReferencesChapter 6 Stopping Time of Invariant Sequential Probability Ratio Tests 1. Introduction 1.1. Purpose of This Chapter 1.2. Simple Hypotheses 1.3. Composite Hypotheses 1.4. Historical Outline 1.5. Outline of the Contents of This Chapter 2. Exponential Boundedness and Exponential Convergence 2.1. Definitions and Properties 2.2. Stein's Lemma and Its Generalization 3. Probability Ratios of Maximal Invariants 3.1. The Integral Ratio Method 3.2. Approximations: Laplace's Method 3.3. Examples of the Laplace Method 4. Derivation of the log Probability Ratio of Several Invariant SPRTs 4.1. Sequential Test of the Standard Deviation in a Normal Population 4.2. Sequential Test of the Covariance Matrix in a Multivariate Normal Population 4.3. Sequential t-Test 4.4. Two-Sided Sequential t-Test 4.5. Sequential F-Test for the General Linear Hypothesis 4.6. Sequential T2-Test for the Mean of a Multivariate Normal Population 4.7.