Recursive methods for statistical prediction with applications

Recursive methods for solving the nonparametric regression problem in the GLIMs and computing the Best Linear Unbiased Predictors are discussed here. An iterated state space algorithm is introduced to compute the generalized smoothing spline estimate, and it is especially useful in calculating the leave-one-out estimates. Two cross validation functions (Kullback-Leibler and least squares cross validation) for estimating the smoothing parameter in the generalized smoothing splines are discussed. The simulation results showed that these two cross validation functions performed quite well.Best Linear Unbiased Predictors can be used to predict the values of a random function from the observed values. It is of interest to have an efficient algorithm to compute the predictions when observations are taken sequentially, rather than performing the linear algebra from the beginning. An updatable algorithm, which is based on combining the updating procedures of Cholesky and Q-R decomposition, is introduced to compute the predictions and mean squared error of the predictions when more observations are taken.U of I OnlyETDs are only available to UIUC Users without author permissio