Statistics for Mathematicians: A Rigorous First Course

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Birkhäuser, Jun 1, 2016 - Mathematics - 177 pages

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.


 

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Contents

1 Regular Probability Models
1
2 Sampling from Probability Distributions
41
3 Point Estimation of Model Parameters
60
4 Tests of Hypotheses for Model Parameters
95
5 Confidence Intervals for Model Parameters
130
Appendix
151
Bibliography
177
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About the author (2016)

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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