Doctor of Philosophy / Department of Statistics / James W. Neill / Checking the adequacy of a proposed parametric nonlinear regression model is important
in order to obtain useful predictions and reliable parameter inferences. Lack of fit is said to
exist when the regression function does not adequately describe the mean of the response
vector. This dissertation considers asymptotics, implementation and a comparative performance
for the likelihood ratio tests suggested by Neill and Miller (2003). These tests use
constructed alternative models determined by decomposing the lack of fit space according to
clusterings of the observations. Clusterings are selected by a maximum power strategy and a
sequence of statistical experiments is developed in the sense of Le Cam. L2 differentiability
of the parametric array of probability measures associated with the sequence of experiments
is established in this dissertation, leading to local asymptotic normality. Utilizing contiguity,
the limit noncentral chi-square distribution under local parameter alternatives is then
derived. For implementation purposes, standard linear model projection algorithms are
used to approximate the likelihood ratio tests, after using the convexity of a class of fuzzy
clusterings to form a smooth alternative model which is necessarily used to approximate the
corresponding maximum optimal statistical experiment. It is demonstrated empirically that
good power can result by allowing cluster selection to vary according to different points along
the expectation surface of the proposed nonlinear regression model. However, in some cases,
a single maximum clustering suffices, leading to the development of a Bonferroni adjusted
multiple testing procedure. In addition, the maximin clustering based likelihood ratio tests
were observed to possess markedly better simulated power than the generalized likelihood
ratio test with semiparametric alternative model presented by Ciprian and Ruppert (2004).
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/2366 |
| Date | January 1900 |
| Creators | Munasinghe, Wijith Prasantha |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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