Statistics for Mathematicians

1. Front Matter

   Pages i-xv

   PDF

2. Regular Probability Models

   • Victor M. Panaretos

   Pages 1-40

3. Sampling from Probability Distributions

   • Victor M. Panaretos

   Pages 41-59

4. Point Estimation of Model Parameters

   • Victor M. Panaretos

   Pages 61-93

5. Tests of Hypotheses for Model Parameters

   • Victor M. Panaretos

   Pages 95-129

6. Confidence Intervals for Model Parameters

   • Victor M. Panaretos

   Pages 131-150

7. Back Matter

   Pages 151-177

   PDF

This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.

 

 

• 62-XX
• confidence intervals
• estimation
• likelihood
• statistical inference
• testing of hypotheses

“The author aims to present a few topics that he considers important, striking an excellent balance between the need to be concise and to include all of the fundamental methods. … this is a valuable book for both mathematics students and applies researchers, and fills a gap in the literature by providing a rigorous and modern introduction to the basic theory of statistics.” (Marco Bee, Mathematical Reviews, February, 2017)

“Panaretos … provides a logical, thorough mathematical representation for a minimally selected number of topics in one-parameter statistical inference. … textbook is appropriate for those students, regardless of their disciplines, interested in learning about or becoming more familiarized with the essence of statistics in a formal and eloquent mathematical framework … . The author offers an extensive list of entry-leveland advanced textbooks in mathematical statistics for further reading … . Summing Up: Recommended. Upper-division undergraduates through researchers and faculty.” (S.-T. Kim, Choice, Vol. 54 (5), January, 2017)

• Institute of Mathematics, EPFL, Lausanne, Switzerland

  Victor M. Panaretos

Victor M. Panaretos is Associate Professor of Mathematical Statistics at the Department of Mathematics of the EPFL. He completed his undergraduate studies in Mathematics and Statistics at the Athens University of Economics and Business and at Trinity College Dublin in 2003. He received a PhD in Statistics from the University of California at Berkeley in 2007, where he studied supported by an NSF Graduate Research Fellowship Award, and received the Erich L. Lehmann Award for an Outstanding Doctoral Dissertation in Theoretical Statistics. He joined the EPFL as an Assistant Professor in 2007 at the age of 24, as the youngest ever faculty of the institution, and was promoted to Associate Professor and tenured in 2013, again the youngest to ever do so. He is the recipient of an ERC Starting Grant Award and an Elected Member of the International Statistical Institute. He has given over 30 invited conference talks and 50 invited seminars. He has served as the Editor of Bernoull

i News, and is an Associate Editor for the Annals of Applied Statistics, Biometrika, and the Electronic Journal of Statistics. He is a member of the Publications Committee of the Bernoulli Society for Mathematical Statistics and Probability.

 

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