Lectures on the Nearest Neighbor Method

“This book deals with different aspects regarding this approach, starting with the standard k-nearest neighbor model, and passing through the weighted k-nearest neighbor model, estimations for entropy, regression functions etc. … It is intended for a large audience, including students, teachers, and researchers.” (Florin Gorunescu, zbMATH 1330.68001, 2016)

• Part I: Density Estimation.- Order Statistics and Nearest Neighbors.- The Expected Nearest Neighbor Distance.- The k-nearest Neighbor Density Estimate.- Uniform Consistency.- Weighted k-nearest neighbor density estimates.- Local Behavior.- Entropy Estimation.- Part II: Regression Estimation.- The Nearest Neighbor Regression Function Estimate.- The 1-nearest Neighbor Regression Function Estimate.- LP-consistency and Stone's Theorem.- Pointwise Consistency.- Uniform Consistency.- Advanced Properties of Uniform Order Statistics.- Rates of Convergence.- Regression: The Noisless Case.- The Choice of a Nearest Neighbor Estimate.- Part III: Supervised Classification.- Basics of Classification.- The 1-nearest Neighbor Classification Rule.- The Nearest Neighbor Classification Rule. Appendix.- Index.