Publication Date

Spring 5-6-1975


The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in this dissertation are then applied to data collected by the University of New Mexico Medical Staff on weight and biparietal diameter of live newborns and fresh abortuses within thirty minutes of birth. A numerical formula is developed for prediction of weight of a fetus or a newborn from its biparie­tal diameter.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

William Zimmer

Second Committee Member

Herbert Thaddeus Davis III

Third Committee Member

Betty Jean Eberle

Fourth Committee Member

Steven Arthur Pruess



Document Type