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Produktbild: An Introduction to Envelopes

An Introduction to Envelopes Dimension Reduction for Efficient Estimation in Multivariate Statistics

Aus der Reihe Wiley Series in Probability and Statistics

179,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

09.10.2018

Verlag

John Wiley & Sons

Seitenzahl

320

Maße (L/B/H)

23,1/15,7/2 cm

Gewicht

635 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-42293-8

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

09.10.2018

Verlag

John Wiley & Sons

Seitenzahl

320

Maße (L/B/H)

23,1/15,7/2 cm

Gewicht

635 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-42293-8

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: An Introduction to Envelopes
  • Preface xv
     
    Notation and Definitions xix
     
    1 Response Envelopes 1
     
    1.1 The Multivariate Linear Model 2
     
    1.1.1 Partitioned Models and Added Variable Plots 5
     
    1.1.2 Alternative Model Forms 6
     
    1.2 Envelope Model for Response Reduction 6
     
    1.3 Illustrations 10
     
    1.3.1 A Schematic Example 10
     
    1.3.2 Compound Symmetry 13
     
    1.3.3 Wheat Protein: Introductory Illustration 13
     
    1.3.4 Cattle Weights: Initial Fit 14
     
    1.4 More on the Envelope Model 19
     
    1.4.1 Relationship with Sufficiency 19
     
    1.4.2 Parameter Count 19
     
    1.4.3 Potential Gains 20
     
    1.5 Maximum Likelihood Estimation 21
     
    1.5.1 Derivation 21
     
    1.5.2 Cattle Weights: Variation of the X-Variant Parts of Y 23
     
    1.5.3 Insights into ÊSigma (B)24
     
    1.5.4 Scaling the Responses 25
     
    1.6 Asymptotic Distributions 25
     
    1.7 Fitted Values and Predictions 28
     
    1.8 Testing the Responses 29
     
    1.8.1 Test Development 29
     
    1.8.2 Testing Individual Responses 32
     
    1.8.3 Testing Containment Only 34
     
    1.9 Nonnormal Errors 34
     
    1.10 Selecting the Envelope Dimension, u 36
     
    1.10.1 Selection Methods 36
     
    1.10.1.1 Likelihood Ratio Testing 36
     
    1.10.1.2 Information Criteria 37
     
    1.10.1.3 Cross-validation 37
     
    1.10.2 Inferring About rank (beta) 38
     
    1.10.3 Asymptotic Considerations 38
     
    1.10.4 Overestimation Versus Underestimation of u 41
     
    1.10.5 Cattle Weights: Influence of u 43
     
    1.11 Bootstrap and Uncertainty in the Envelope Dimension 45
     
    1.11.1 Bootstrap for Envelope Models 45
     
    1.11.2 Wheat Protein: Bootstrap and Asymptotic Standard Errors, u Fixed 46
     
    1.11.3 Cattle Weights: Bootstrapping u 47
     
    1.11.4 Bootstrap Smoothing 48
     
    1.11.5 Cattle Data: Bootstrap Smoothing 49
     
    2 Illustrative Analyses Using Response Envelopes 51
     
    2.1 Wheat Protein: Full Data 51
     
    2.2 Berkeley Guidance Study 51
     
    2.3 Banknotes 54
     
    2.4 Egyptian Skulls 55
     
    2.5 Australian Institute of Sport: Response Envelopes 58
     
    2.6 Air Pollution 59
     
    2.7 Multivariate Bioassay 63
     
    2.8 Brain Volumes 65
     
    2.9 Reducing Lead Levels in Children 67
     
    3 Partial Response Envelopes 69
     
    3.1 Partial Envelope Model 69
     
    3.2 Estimation 71
     
    3.2.1 Asymptotic Distribution of 72
     
    3.2.2 Selecting u1 73
     
    3.3 Illustrations 74
     
    3.3.1 Cattle Weight: Incorporating Basal Weight 74
     
    3.3.2 Mens' Urine 74
     
    3.4 Partial Envelopes for Prediction 77
     
    3.4.1 Rationale 77
     
    3.4.2 Pulp Fibers: Partial Envelopes and Prediction 78
     
    3.5 Reducing Part of the Response 79
     
    4 Predictor Envelopes 81
     
    4.1 Model Formulations 81
     
    4.1.1 Linear Predictor Reduction 81
     
    4.1.1.1 Predictor Envelope Model 83
     
    4.1.1.2 Expository Example 83
     
    4.1.2 Latent Variable Formulation of Partial Least Squares Regression 84
     
    4.1.3 Potential Advantages 86
     
    4.2 SIMPLS 88
     
    4.2.1 SIMPLS Algorithm 88
     
    4.2.2 SIMPLS When n
     
    4.2.2.1 Behavior of the SIMPLS Algorithm 90
     
    4.2.2.2 Asymptotic Properties of SIMPLS 91
     
    4.3 Likelihood-Based Predictor Envelopes 94
     
    4.3.1 Estimation 95
     
    4.3.2 Comparisions with SIMPLS and Principal Component Regression 97
     
    4.3.2.1 Principal Component Regression 98
     
    4.3.2.2 SIMPLS 98
     
    4.3.3 Asymptotic Properties 98
     
    4.3.4 Fitted Values and Prediction 100