Date of Graduation

Spring 2013

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

George Mathew

Abstract

In a regression problem the relationship between an explanatory variable X and a response variable Y may be expressed as E(Y|X = x) = m(x), where m(x) is some unknown function estimated based on random sample of pairs of observations on (X, Y). In a parametric approach m(x) is a function that can be fully described by a finite set of parameters. In practice, there are many situations where such a curve may not describe the data at all. In such a case a nonparametric approach to estimate m(x) without reference to a specific functional form may be employed. In this thesis, we adopt a nonparametric approach, known as kernel regression. Adopting results from kernel density estimation, expressions for bias, variance, and related properties of Nadaraya-Watson kernel regression estimator are derived. The confidence bands based on the estimator are also derived. The procedure is applied to a simulated data and also to two real data sets. It is shown that only a nonparametric approach is suitable in one of the real data sets. The confidence bands for the estimated smoothing curve are also provided in each situation.

Keywords

nonparametric regression, kernel density estimation, kernel regression, Nadaraya-Watson estimator, band width, bias, variance, confidence band

Subject Categories

Mathematics

Copyright

© Rebekah Elizabeth Austin

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