#### Thesis Title

#### Date of Graduation

Summer 2013

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

George Mathew

#### Keywords

continuous functions, confidence bands, nonparametric regression, polynomial splines, knots, modulus of continuity, spline accuracy theorem

#### Subject Categories

Mathematics

#### Abstract

Suppose (X₁,Y₁), (X₂,Y₂),...,(Xn,Yn) be a sample of observations on two variables X and Y. One of the procedures to analyze such a data set is to arrive at a functional relation of the form Y = f(X) + e , where X is treated as the explanatory variable, Y is treated as the response variable and e is the random error involved. In the parametric regression approach the function f(X) is assumed to belong to a class of functions which can be described by a finite number of parameters. The nonparametric approach is to choose the function f from some smooth family of functions. It is almost impossible to arrive at a smooth function f to describe the relation between X and Y based on observed values of (X, Y). In this thesis methods to approximate a function f by low-order polynomial spline functions are provided. In particular, methods to approximate f by first, second and third degree polynomial splines are provided in detail. A proof of spline accuracy theorem is also established. The procedure is applied to arrive at a nonparametric regression curve and confidence bands for both simulated and real data sets.

#### Copyright

© Rosemary Dee Sherwood Green

#### Recommended Citation

Green, Rosemary Dee Sherwood, "Applications of Splines in Nonparametric Regression" (2013). *MSU Graduate Theses*. 1651.

https://bearworks.missouristate.edu/theses/1651

**Campus Only**