Essentials of probability theory for statisticians. (2016)

• Record Type: Book
• Further Information: Note: Michael A. Proschan and Pamela A. Shaw.
• Authors: Proschan, Michael A; Shaw, Pamela, 1968-
• Contents: Introduction; Why More Rigor Is Needed Size Matters ; Cardinality; Summary The Elements of Probability Theory ; Introduction; Sigma-Fields; The Event That An Occurs Infinitely Often; Measures/Probability Measures; Why Restriction of Sets Is Needed; When We Cannot Sample Uniformly; The Meaninglessness of Post-Facto Probability Calculations; Summary Random Variables and Vectors ; Random Variables; Random Vectors; The Distribution Function of a Random Variable; The Distribution Function of a Random Vector; Introduction to Independence; Take (Ω, F, P ) = ((0, 1), B (0, 1), μL ), Please!; Summary Integration and Expectation ; Heuristics of Two Different Types of Integrals; Lebesgue–Stieltjes Integration; Properties of Integration; Important Inequalities; Iterated Integrals and More on Independence; Densities; Keep It Simple; Summary Modes of Convergence ; Convergence of Random Variables; Connections between Modes of Convergence; Convergence of Random Vectors; Summary Laws of Large Numbers ; Basic Laws and Applications; Proofs and Extensions; Random Walks; Summary Central Limit Theorems ; CLT for iid Random Variables and Applications; CLT for Non iid Random Variables; Harmonic Regression; Characteristic Functions; Proof of Standard CLT; Multivariate Ch.f.s and CLT; Summary More on Convergence in Distribution ; Uniform Convergence of Distribution Functions; The Delta Method ; Convergence of Moments: Uniform Integrability; Normalizing Sequences; Review of Equivalent Conditions for Weak Convergence; Summary Conditional Probability and Expectation ; When There Is a Density or Mass Function; More General Definition of Conditional Expectation; Regular Conditional Distribution Functions; Conditional Expectation as a Projection; Conditioning and Independence; Sufficiency; Expect the Unexpected from Conditional Expectation; Conditional Distribution Functions as Derivatives; Appendix: Radon–Nikodym Theorem; Summary Applications ; F(X) ~ U [0, 1] and Asymptotics; Asymptotic Power and Local Alternatives; Insufficient Rate of Convergence in Distribution; Failure to Condition on All Information; Failure to Account for the Design; Validity of Permutation Tests: I; Validity of Permutation Tests: II; Validity of Permutation Tests III; A Brief Introduction to Path Diagrams; Estimating the Effect Size; Asymptotics of an Outlier Test; An Estimator Associated with the Logrank Statistic Appendix A: Whirlwind Tour of Prerequisites; Appendix B: Common Probability Distributions; Appendix C: References; Appendix D: Mathematical Symbols and Abbreviations Index
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 519.201; Probabilities; Mathematical statistics
• Languages: English
• ISBNs: 9781498704229; 9781498704205; 9781498704212
• Related ISBNs: 9781498704199
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.