UNITED STATISTICAL ALGORITHMS, LP COMOMENTS, COPULA DENSITY, NONPARAMETRIC MODELING

In addition to solving problems \retail" (one at a time for one client/collaborator), academic statistics should aim to solve problems \wholesale"(algorithms and computer code that can be applied for many clients). We call this approach to teaching and practice SMART COMPUTATIONAL STATISTICS = united data science algorithms providing methods for Small Data and Big Data. It practices that the goal of computing is insight (from graphical presentations) rather than numbers (especially accurate numbers which can be suboptimal (right answer to wrong question)). Our extensive theory simultaneously extends and integrates traditional (classical) statistical methods, treats multivariate discrete and continuous variables, parametric and nonparametric modeling, classication and measuring dependence relationships of ( X;Y ) where X can be a high dimensional vector of features and Y a scalar variable to predict or classify. The goal of this paper is to gently introduce many basic concepts: quantile; mid-distribution; mid-quantile; comparison density; comparison distribution; skew-G distribution; LP coecients, moments, co-moments; orthonormal score functions series density estimation; custom construction of mid-distribution based score functions; comparison probability version of Bayes theorem; copula density function series nonparametric estimation. The practice of these algorithms is illustrated with examples of real data.