Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Statistics have been derived for detecting one-sided and two- sided parameter changes at unknown times in regression models. The statistic for detecting one-sided changes is a linear function of regression residuals whereas the statistic for detecting two-sided changes is a quadratic form in the regression residuals. Under the assumption that the regressor functions are continuously differentiable, the asymptotic distribution of the quadratic form;is shown to be that of a sum of random variables which are stochastic integrals of the form;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);where B(,p)(t), t (epsilon) 0,1 is the limit process for the sequence of stochastic processes defined on partial sums of appropriate functions of regression residuals. The limit processes are found to be functions of Brownian Motion process. The distributions of these stochastic integrals are found by solving Fredholm integral equations defined on the covariance kernels of the limit processes. Explicit analytic solutions are obtained when the regressor functions are trigonometric. Limit processes defined on non-linear regression residuals are shown to be functions of Brownian Motion, and the distributions of the stochastic integrals based on these limit processes are derived when the non-linear regressor functions are of exponential type. These distributions have applications to detect parameter changes at unknown times in non-linear regression models.



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