Probability for Statisticians by Galen R. Shorack
Home > Science & Mathematics > Mathematics > Optimization > Probability for Statisticians
Probability for Statisticians

Probability for Statisticians


     0     
5
4
3
2
1



International Edition


About the Book

PrefaceUse of This TextDefinition of Symbols
Chapter 1. Measures

  1. Basic Properties of Measures
  2. Construction and Extension of Measures
  3. Lebesgue Stieltjes Measures
Chapter 2. Measurable Functions and Convergence
  1. Mappings and σ-Fields
  2. Measurable Functions
  3. Convergence
  4. Probability, RVs, and Convergence in Law
  5. Discussion of Sub σ-Fields
Chapter 3. Integration
  1. The Lebesgue Integral
  2. Fundamental Properties of Integrals
  3. Evaluating and Differentiating Integrals
  4. Inequalities
  5. Modes of Convergence
Chapter 4 Derivatives via Signed Measures
  1. Introduction
  2. Decomposition of Signed Measures
  3. The Radon Nikodym Theorem
  4. Lebesgue's Theorem
  5. The Fundamental Theorem of Calculus
Chapter 5. Measures and Processes on Products
  1. Finite-Dimensional Product Spaces
  2. Random Vectors on (Ω, Α, P)
  3. Countably Infinite Product Probability Spaces
  4. Random Elements and Processes on (Ω, Α, P)
Chapter 6. Distribution and Quantile Functions
  1. Character of Distribution Functions
  2. Properties of Distribution Functions
  3. The Quantile Transformation
  4. Integration by Parts Applied to Moments
  5. Important Statistical Quantities
  6. Infinite Variances
Chapter 7. Independence and Conditional Distributions
  1. Independence
  2. The Tail σ-Field
  3. Uncorrelated Random Variables
  4. Basic Properties of Conditional Expectation
  5. Regular Conditional Probability
Chapter 8. WLLN, SLLN, LIL, and Series
  1. Introduction
  2. Borel Cantelli and Kronecker Lemmas
  3. Truncation, WLLN, and Review of Inequalities
  4. Maximal Inequalities and Symmetrization
  5. The Classical Laws of Large Numbers (or, LLNs)
  6. Applications of the Laws of Large Numbers
  7. Law of the Iterated Logarithm (or, LIL)
  8. Strong Markov Property for Sums of IID RVs
  9. Convergence of Series of Independent RVs
  10. Martinagles
  11. Maximal Inequalities, Some with ↗ Boundaries
Chapter 9. Characteristic Functions and Determining Classes
  1. Classical Convergence in Distribution
  2. Determining Classes of Functions
  3. Characteristic Functions, with Basic Results
  4. Uniqueness and Inversion
  5. The Continuity Theorem
  6. Elementary Complex and Fourier Analysis
  7. Esseen's Lemma
  8. Distributions on Grids
  9. Conditions for Ø to Be a Characteristic Function
Chapter 10. CLTs via Characteristic Functions
  1. Introduction
  2. Basic Limit Theorems
  3. Variations on the Classical CLT
  4. Examples of Limiting Distributions
  5. Local Limit Theorems
  6. Normality Via Winsorization and Truncation
  7. Identically Distributed RVs
  8. A Converse of the Classical CLT
  9. Bootstrapping
  10. Bootstrapping with Slowly ↗ Winsorization
Chapter 11. Infinitely Divisible and Stable Distributions
  1. Infinitely Divisible Distributions
  2. Stable Distributions
  3. Characterizing Stable Laws
  4. The Domain of Attraction of a Stable Law
  5. Gamma Approximations
  6. Edgeworth Expansions
Chapter 12. Brownian Motion and Empirical Processes
  1. Special Spaces
  2. Existence of Processes on (C, C) and (D, D)
  3. Brownian Motion and Brownian Bridge
  4. Stopping Times
  5. Strong Markov Property
  6. Embedding a RV in Brownian Motion
  7. Barrier Crossing Probabilities
  8. Embedding the Partial Sum Process
  9. Other Properties of Brownian Motion
  10. Var
    About the Author:

    Galen Shorack, PhD, is Professor Emeritus in the Department of Statistics (of which he was a founding member) and Adjunct Professor in the Department of Mathematics at the University of Washington, Seattle. He received his Bachelor of Science and Master of Science degrees in Mathematics from the University of Oregon and his PhD in Statistics from Stanford University. Dr. Shorack's research interests include limit theorems in statistics, the theory of empirical processes, trimming-Winsorizing, and regular variation. He has served as Associate Editor of the Annals of Mathematical Statistics (Annals of Statistics) and is Fellow of the Institute of Mathematical Statistics.


Best Sellers



Product Details
  • ISBN-13: 9783319522067
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 0002-2017
  • Language: English
  • Returnable: Y
  • Spine Width: 27 mm
  • Width: 178 mm
  • ISBN-10: 331952206X
  • Publisher Date: 03 Oct 2017
  • Binding: Paperback
  • Height: 254 mm
  • No of Pages: 510
  • Series Title: Springer Texts in Statistics
  • Weight: 965 gr


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Probability for Statisticians
Springer -
Probability for Statisticians
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Probability for Statisticians

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals



    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!