@MISC{n.n._preliminarymaterial, author = {n.n.}, title = {Preliminary material for APTS Nonparametric Smoothing module }, year = {} }

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Abstract

Density estimation and regression problems are two of the most important types of problem encountered by statisticians. Nonparametric approaches to these problems have gained enormous popularity in the last fifty years or so, as they make far weaker assumptions than parametric methods. In this module, we introduce some of the fundamental nonparametric techniques. We aim to understand these methods in both theory and practice. Basic properties of statistical estimators in parametric contexts (bias, variance, mean squared error etc.), familiarity with standard statistical models (e.g. the linear model and weighted least squares), and a general comfort with basic concepts in analysis and probability will be assumed. Measure theory is not necessary, though this will mean that some of the proofs will be a little longer than would otherwise be the case, and I may include occasional optional exercises for people who are familiar with this material. On the computational side, basic familiarity with R will also be assumed. Those who have been to the Statistical Computing module will certainly have sufficient background here.