Anirban DasGupta Professor of Statistics [email protected] Address: 150 N. University Street MATH 528 West Lafayette, IN 47907-2068 Phone: (765) 494-6033 Fax: (765) 494-0558

Anirban DasGupta August, 2011 Education PhD, Indian Statistical Institute, Calcutta, 1984 MStat, Indian Statistical Institute, Calcutta, 1978 BStat(Hons.), Indian Statistical Institute, Calcutta, 1977. PhD Course Work at the Indian Statistical Institute Calculus, Vector calculus, Advanced geometry, Mechanics, Theory of vec-

Probability for Statistics and Machine Learning: Fundamentals and Advanced Topics Anirban DasGupta

Anirban DasGupta. Professor of Statistics E-mail: [email protected]; Homepage: https://www.stat.purdue.edu/~dasgupta; Office: MATH 528; Phone: 765-494-6033; Fax: 765-494-0558; Research Interests. Asymptotics; Probability Inequalities; Probability and Analysis; Previous Ph.D. Students from Purdue University Department of Statistics. Sanjib ...

Contents 1 Introducing Probability 5 1.1 ExperimentsandSampleSpaces..... 6 1.2 Set Theory Notation and Axioms of Probability . . . . . . . . . . . 7

Anirban DasGupta Purdue University, USA Abstract The maximum cell frequency in a multinomial distribution is of current in-terest in several areas of probability and statistics. Difierent asymptotics apply for difierent rates of growth for the number of cells and the number of units.

Anirban DasGupta, Larry Shepp November 24, 2012 AbstractLet X n×1 be an n-dimensional Gaussian vector with mean zero and covari-ance matrix Σ. We use Fourier techniques and special functions to study the density of the L p norm of X, namely ||X|| p = (P n i=1 |X i| p)1/p,0 < p < ∞. A two term asymptotic

Contents 1 Basic Convergence Concepts and Theorems 10 1.1 Some Basic Notation and Convergence Theorems . . . . . . . . . . 10 1.2 Three Series Theorem and Kolmogorov ...

Anirban DasGupta and S. N. Lahiri June 15, 2012 Abstract We consider a novel sparse signal detection problem which natu-rally combines complexities of a binomial inference problem with elements of estima-tion of a smooth nonparametric monotone function. Thus, the problem is inherently semiparametric.

Anirban DasGupta Purdue University, West Lafayette, IN JULY 29,2005 AMS Subject Classi cations : Primary 60E07; Secondary 62F10 Key words and Phrases : Ancillary, Basu’s theorem, Completeness, Fac-torization, Goldie-Steutel law, Independent, …