Smoothing Spline Analysis of Variance for Polychotomous Response Data

This thesis discusses the use of penalized likelihood methods in the k-category case to estimate (p_1(x), ..., p_k(x)) where x is the attribute vector, and p_r is the estimated probability that a subject with attribute x is in category r, and generalizes Wahba et al, NIPS v. 6 (1994) (note added 2002 by G. Wahba): This approach parallells the multicategory support vector machine (MSVM) of Lee, Lin and Wahba (2001, TR 1043), and may be considered in the case where the p_r are bounded away from 0 or 1 and the training set observations are relatively dense, while the multicategory support vector machine may be considered where x is high dimensional, data is sparse and/or there are substantial regions with the true p's near 0 or 1.).