A study of random field models in fitting unspecified data generating processes: Theory and applications
Abstract
The purpose of this work is to establish the asymptotic theory for the random field model applied in the general statistical modeling activities in the misspecification setting. New convergent results are shown to replace the conventional Law of Large Numbers, which is not directly applicable to the misspecified random field models. If the true data generating process is additive, we propose an additive random field model with better out of sample prediction power. A proportional additive random field model is introduced to reduce the model estimation computing demand. In the end, a parametric residual based additivity test is constructed. Monte Carlo simulations show the promising applications of the asymptotic theory, the new methodology and the additivity test for samples with small to moderate sizes.
Degree
Ph.D.
Advisors
Song, Purdue University.
Subject Area
Statistics|Economic theory
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