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Format: 1 Online-Ressource (xxii, 354 Seiten) : , Illustrationen.

ISBN: 978-3-030-34675-1

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34674-4

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34676-8

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34677-5

Language: English

Keywords: Aufsatzsammlung ; Aufsatzsammlung ; Festschrift

DOI: 10.1007/978-3-030-34675-1

URL: Volltext  (URL des Erstveröffentlichers)

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

UID:

Format: 1 Online-Ressource (xxii, 354 Seiten) : , Illustrationen.

ISBN: 978-3-030-34675-1

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34674-4

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34676-8

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34677-5

Language: English

Keywords: Aufsatzsammlung

DOI: 10.1007/978-3-030-34675-1

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 Online-Ressource (xxii, 354 Seiten) : , Illustrationen.

ISBN: 978-3-030-34675-1

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34674-4

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34676-8

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-34677-5

Language: English

Keywords: Aufsatzsammlung

DOI: 10.1007/978-3-030-34675-1

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: XXII, 354 p. 34 illus. , online resource.

Edition: 1st ed. 2020.

ISBN: 9783030346751

Content: This book commemorates the scientific contributions of distinguished statistician, Andrei Yakovlev. It reflects upon Dr. Yakovlev's many research interests including stochastic modeling and the analysis of micro-array data and throughout the book it emphasizes applications of the theory in biology, medicine and public health. The contributions to this volume are divided into two parts. Part A consists of original research articles, which can be roughly grouped into four thematic areas, (i) branching processes, especially as models for cell kinetics, (ii) multiple testing issues as they arise in the analysis of biologic data, (iii) applications of mathematical models and of new inferential techniques in epidemiology, and (iv) contributions to statistical methodology, with an emphasis on the modeling and analysis of survival time data. Part B consists of methodological research reported as a short communication, ending with some personal reflections on research fields associated with Andrei and on his approach to science. The Appendix contains an abbreviated vitae and a list of Andrei's publications, complete as far as we know. The contributions in this book are written by Dr. Yakovlev's collaborators and notable statisticians including former Presidents of the Institute of Mathematical Statistics and of the Statistics Section of the AAAS. Dr. Yakovlev's research appeared in four books and almost 200 scientific papers, in mathematics, statistics, biomathematics and biology journals. Ultimately this book offers a tribute to Dr. Yakovlev's work and recognizes the legacy of his contributions in the biostatistics community.

Note: Chapter 1. Stochastic Models of Cell Proliferation Kinetics based on Branching Processes -- Chapter 2. Age-Dependent Branching Processes with Non-Homogeneous Poisson Immigration as Models of Cell Kinetics -- Chapter 3. A Study of the Correlation Structure of Microarray Gene Expression Data Based on Mechanistic Modeling of Cell Population Kinetics -- Chapter 4. Correlation Between the True and False Discoveries in a Positively Dependent Multiple Comparison Problem -- Chapter 5. Multiple Testing Procedures: Monotonicity and Some of Its Implications -- Chapter 6. Applications of Sequential Methods in Multiple Hypothesis Testing -- Chapter 7. Multistage Carcinogenesis: A Unified Framework for Cancer Data Analysis -- Chapter 8. A Machine-Learning Algorithm for Estimating and Ranking the Impact of Environmental Risk Factors in Exploratory Epidemiological Studies -- Chapter 9. A Latent Time Distribution Model for the Analysis of Tumor Recurrence Data: Application to the Role of Age in Breast Cancer -- Chapter 10. Estimation of Mean Residual Life -- Chapter 11. Likelihood Transformations and Artificial Mixtures -- Chapter 12. On the Application of Flexible Designs when Searching for the Better of Two Anticancer Treatments -- Chapter 13. Parameter Estimation for Multivariate Nonlinear Stochastic Differential Equation Models: A Comparison Study -- Chapter 14. On Frailties, Archimedean Copulas and Semi-Invariance Under Truncation -- Chapter 15. The Generalized ANOVA - A Classic Song Sung with Modern Lyrics -- Chapter 16. Analyzing Gene Pathways from Microarrays to Sequencing Platforms -- Chapter 17. A New Approach for Quantifying Uncertainty in Epidemiology -- Chapter 18. Branching Processes: A Personal Historical Perspective -- Chapter 19. Principles of Mathematical Modeling in Biomedical Sciences: An Unwritten Gospel of Andrei Yakovlev.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030346744

Additional Edition: Printed edition: ISBN 9783030346768

Additional Edition: Printed edition: ISBN 9783030346775

Language: English

DOI: 10.1007/978-3-030-34675-1

URL: https://doi.org/10.1007/978-3-030-34675-1

UID:

Format: 1 online resource (472 pages)

Edition: First edition.

ISBN: 9781003049340 , 1003049346 , 9781000488012 , 1000488012 , 9781000488074 , 1000488071

Series Statement: Chapman & Hall texts in statistical science

Content: "The purpose of applying mathematical theory to the theory of statistical inference is to make it simpler and more elegant. Theory of Statistical Inference is concerned with the development of a type of optimization theory which can be used to inform the choice of statistical methodology. Of course, this would be pointless without reference to such methods. We are simply noting that they are included in support of the larger goal. This book distinguishes itself from other graduate textbooks because it is written from the point of view that some degree of understanding of measure theory, as well as other branches of mathematics, which include topology, group theory and complex analysis, should be a part of the canon of statistical inference"--

Note: Preface 1 Distribution Theory 1.1 Introduction1.2 Probability Measures1.3 Some Important Theorems of Probability1.4 Commonly Used Distributions1.5 Stochastic Order Relations1.6 Quantiles1.7 Inversion of the CDF1.8 Transformations of Random Variables1.9 Moment Generating Functions1.10 Moments and Cumulants1.11 Problems2 Multivariate Distributions2.1 Introduction2.2 Parametric Classes of Multivariate Distributions2.3 Multivariate Transformations2.4 Order Statistics2.5 Quadratic Forms, Idempotent Matrices and Cochran's Theorem2.6 MGF and CGF of Independent Sums2.7 Multivariate Extensions of the MGF2.8 Problems3 Statistical Models3.1 Introduction3.2 Parametric Families for Statistical Inference3.3 Location-Scale Parameter Models3.4 Regular Families3.5 Fisher Information3.6 Exponential Families3.7 Sufficiency3.8 Complete and Ancillary Statistics3.9 Conditional Models and Contingency Tables3.10 Bayesian Models3.11 Indifference, Invariance and Bayesian Prior Distributions3.12 Nuisance Parameters3.13 Principles of Inference3.14 Problems4 Methods of Estimation4.1 Introduction4.2 Unbiased Estimators4.3 Method of Moments Estimators4.4 Sample Quantiles and Percentiles4.5 Maximum Likelihood Estimation4.6 Confidence Sets4.7 Equivariant Versus Shrinkage Estimation4.8 Bayesian Estimation4.9 Problems5 Hypothesis Testing5.1 Introduction5.2 Basic Definitions5.3 Principles of Hypothesis Tests5.4 The Observed Level of Significance (P-Values)5.5 One and Two Sided Tests5.6 Hypothesis Tests and Pivots5.7 Likelihood Ratio Tests5.8 Similar Tests5.9 Problems6 Linear Models6.1 Introduction6.2 Linear Models - Definition6.3 Best Linear Unbiased Estimators (BLUE)6.4 Least-squares Estimators, BLUEs and Projection Matrices6.5 Ordinary and Generalized Least-Squares Estimators6.6 ANOVA Decomposition and the F Test for Linear Models6.7 The F Test for One-Way ANOVA6.8 Simultaneous Confidence Intervals6.9 Multiple Linear Regression6.10 Problems7 Decision Theory7.1 Introduction7.2 Ranking Estimators by MSE7.3 Prediction7.4 The Structure of Decision Theoretic Inference7.5 Loss and Risk7.6 Uniformly Minimum Risk Estimators (The Location-Scale Model7.7 Some Principles of Admissibility7.8 Admissibility for Exponential Families (Karlin's Theorem)7.9 Bayes Decision Rules7.10 Admissibility and Optimality7.11 Problems8 Uniformly Minimum Variance Unbiased (UMVU) Estimation8.1 Introduction8.2 Definition of UMVUE's8.3 UMVUE's and Sufficiency8.4 Methods of Deriving UMVUEs8.5 Nonparametric Estimation and U-statistics8.6 Rank Based Measures of Correlation8.7 Problems9 Group Structure and Invariant Inference9.1 Introduction9.2 MRE Estimators for Location Parameters9.3 MRE Estimators for Scale Parameters9.4 Invariant Density Families9.5 Some Applications of Invariance9.6 Invariant Hypothesis Tests9.7 Problems10 The Neyman-Pearson Lemma10.1 Introduction10.2 Hypothesis Test as Decision Rules10.3 Neyman-Pearson (NP) Tests10.4 Monotone Likelihood Ratios (MLR)10.5 The Generalized Neyman-Pearson Lemma10.6 Invariant Hypothesis Tests10.7 Permutation Invariant Tests10.8 Problems11 Limit Theorems11.1 Introduction11.2 Limits of Sequences of Random Variables11.3 Limits of Expected Values11.4 Uniform Integrability11.5 The Law of Large Numbers11.6 Weak Convergence11.7 Multivariate Extensions of Limit Theorems11.8 The Continuous Mapping Theorem11.9 MGFs, CGFs and Weak Convergence11.10 The Central Limit Theorem for Triangular Arrays11.11 Weak Convergence of Random Vectors11.12 Problems12 Large Sample Estimation - Basic Principles12.1 Introduction12.2 The _-Method12.3 Variance Stabilizing Transformations12.4 The _-Method and Higher Order Approximations12.5 The Multivariate _-Method12.6 Approximating the Distributions of Sample Quantiles: The Bahadur Representation Theorem12.7 A Central Limit Theorem for U-statistics12.8 The Information Inequality12.9 Asymptotic Efficiency12.10 Problems13 Asymptotic Theory for Estimating Equations13.1 Introduction13.2 Consistency and Asymptotic Normality of M-estimators13.3 Asymptotic Theory of MLEs13.4 A General Form for Regression Models13.5 Nonlinear Regression13.6 Generalized Linear Models (GLMs)13.7 Generalized Estimating Equations (GEE)13.8 Consistency of M-estimators13.9 Asymptotic Distribution of ˆ_n 13.10 Regularity Conditions for Estimating Equations13.11 Problems14 Large Sample Hypothesis Testing14.1 Introduction14.2 Model Assumptions14.3 Large Sample Tests for Simple Hypotheses14.4 Nuisance Parameters and Composite Null Hypotheses14.5 A Comparison of the LR, Wald and Score Tests14.6 Pearson's _2 Test for Independence in Contingency Tables14.7 Estimating Power for Approximate _2 Tests14.8 ProblemsA Parametric Classes of DensitiesB Topics in Linear AlgebraB.1 NumbersB.2 Equivalence RelationsB.3 Vector SpacesB.4 MatricesB.5 Dimension of a Subset of Rd C Topics in Real Analysis and Measure TheoryC.1 Metric spacesC.2 Measure TheoryC.3 IntegrationC.4 Exchange of Integration and DifferentiationC.5 The Gamma and Beta FunctionsC.6 Stirling's Approximation of the FactorialC.7 The Gradient Vector and the Hessian MatrixC.8 Normed Vector SpacesC.9 Taylor's TheoremD Group TheoryD.1 Definition of a GroupD.2 SubgroupsD.3 Group HomomorphismsD.4 Transformation GroupsD.5 Orbits and Maximal InvariantsBibliographyIndex

Language: English

Keywords: Electronic books.

URL: https://www.taylorfrancis.com/books/9781003049340