Skip to main content

A Few Key Probability Theory Results

  • Chapter
  • First Online:
Statistical Inference Under Mixture Models

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

  • 202 Accesses

Abstract

The materials presented in this book are undeniably technical in nature. We established numerous theoretical conclusions by relying on classical probability theory results. Although these conclusions are well-known, many of us often struggle to recall the exact details. Notably, these conclusions are sometimes quoted from papers or books without specifying their applicability to a given context, making it challenging to ensure that the required conditions are met. Chapter 17 compiles some of these cited conclusions from the previous chapters to facilitate reference and ensure clarity regarding their specific contexts.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Bickel, P.J., and K. A. Doksum. 2015. Mathematical Statistics: Basic Ideas and Selected Topics, vol. 2. Boca Raton: CRC Press.

    Book  MATH  Google Scholar 

  • Billingsley, P. 2008. Probability and Measure. Hoboken: Wiley.

    MATH  Google Scholar 

  • Doob, J. L. 1953. Stochastic Processes. Hoboken: Wiley.

    MATH  Google Scholar 

  • Pollard, D. (2012). Convergence of Stochastic Processes. Cham: Springer Science & Business Media.

    MATH  Google Scholar 

  • Rubin, H. 1956. Uniform convergence of random functions with applications to statistics. The Annals of Mathematical Statistics 27: 200–203.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chen, J. (2023). A Few Key Probability Theory Results. In: Statistical Inference Under Mixture Models. ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-99-6141-2_17

Download citation

Publish with us

Policies and ethics