#### Thesis Title

#### Date of Graduation

Spring 2013

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

George Mathew

#### Keywords

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

#### Subject Categories

Mathematics

#### 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.

#### Copyright

© Rebekah Elizabeth Austin

#### Recommended Citation

Austin, Rebekah Elizabeth, "A Method of Kernel Regression" (2013). *MSU Graduate Theses*. 1647.

http://bearworks.missouristate.edu/theses/1647