Discrete Associated-Kernels for Smoothings

Discrete Associated-Kernels for Smoothings: Theory, Methods, and Applications provides a comprehensive exploration of discrete smoothing using associated-kernels. It offers an overview of the theory and relevant analyses in several real-world scenarios.

It begins with a brief history of discrete kernel smoothing and an introduction to popular continuous, asymmetric, and associated kernels. Methods to smooth various discrete, continuous, and mixed functions are covered, including regression, weighting, and discrimination. The univariate, multivariate, and recursive versions are discussed within three families of associated-kernels: categorical, count, and other discretes. The book presents several properties through nonparametric and semiparametric approaches, such as using finite differences for bias in discrete functions, selecting bandwidths by considering the local Bayesian method instead of the adaptive method used for continuous cases, and using normalized estimators for probability density or mass functions. Finally, the book addresses mixed functions on the same univariate support (i.e., time scale) and mixture functions in a multivariate setup (e.g., discrimination analysis). Numerical illustrations and practical applications facilitate understanding of these approaches. Each of the seven chapters concludes with exercises and open problems.

The book is ideal for researchers, as well as master's and doctoral program students and applied statistics professionals. It provides readers with the necessary tools to efficiently analyze data sets.

Key Features

• Rigorous construction methods of associated-kernels
• Comparatives tools and approaches for discrete, continuous and mixte kernel smoothings
• Includes (advanced) practical exercises in \textsf{R} with detailed solutions
• Brings a new view for smoothers of any functional defined on a given (fixed or estimated) support, such as (un)bounded, simplex, half-spaces, cone of positive definite matrices