Date of Graduation

Summer 2013


Master of Science in Mathematics



Committee Chair

George Mathew


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.


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

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