Date of Graduation

Summer 2013

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

George Mathew

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.

Keywords

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

Subject Categories

Mathematics

Copyright

© Rosemary Dee Sherwood Green

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