This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus....

This book approaches the elementary statistical concepts. It presents also some statistical methods of collecting and analysis of data.

AbstractThe following sections are included:IntroductionIntegrationIntegrals on Abstract Measure SpacesIntegrals on Sets of Real NumbersProperties of E(·)Expectations as Informative FunctionalsMoments of Random VariablesGenerating FunctionsConditional ExpectationMoments of Conditional...

Despite the widespread use of graphs in empirical research, little is known about readers' ability to process the statistical information they are meant to convey ("visual inference"). We study visual inference within the context of regression discontinuity (RD) designs by measuring how...

The purpose of this article is to propose that we focus the teaching of the introductory statistics course not merely on the statistical tools to be studied, but on the scientific thinking that they engender. Students must be taught that science is based on the testing of theories and shown how...

Despite the widespread use of graphs in empirical research, little is known about readers' ability to process the statistical information they are meant to convey ("visual inference"). We study visual inference within the context of regression discontinuity (RD) designs by measuring how...

Nonparametric estimators are widely used to estimate the productive efficiency of firms and other organizations, but often without any attempt to make statistical inference. Recent work has provided statistical properties of these estimators as well as methods for making statistical inference,...

Statistical inferences for weights of the global minimum variance portfolio (GMVP) are of both theoretical and practical relevance for mean-variance portfolio selection. Daily realized GMVP weights depend only on realized covariance matrix computed from intraday highfrequency returns. In this...

Motivated by Manski and Tamer (2002) and especially their partial identification analysis of the regression model where one covariate is only interval-measured, we present two extensions. Manski and Tamer (2002) propose two estimation approaches in this context, focussing on general results. The...

As I document using evidence from a journal data repository that I manage, the datasets used in empirical work are getting larger. When we use very large datasets, it can be dangerous to rely on standard methods for statistical inference. In addition, we need to worry about computational issues....