A matrix exponential and bootstrap analysis of nonlinear least squares estimation for compartmental models /
| Main Author: | |
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1991.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | In this research, we are interested in applying the matrix exponential and bootstrap approaches to the analysis of nonlinear least squares estimation for compartment models. We propose a new model with multiplicative errors for a deterministic two-compartment biological system in the area of pharmacokinetics. Large correlation and large asymptotic variance of estimates of parameters in compartmental models can cause estimation and inference problems in the analysis of the mean residence time (MRT). We estimate the MRT's using nonlinear least squares and utilize the iterated-once bootstrap percentile-t method to form confidence intervals for MRT's. Also, we apply asymptotic normal theory to construct asymptotic confidence intervals for MRT's. We develop computational methods for the two-compartment model and analyze the tetracycline data from Wagner (1967). For the nonlinear least squares estimation, we modify Levenberg-Marquardt (IMSL 1982) and Newton-Raphson (Press et al. 1985) numerical routines to obtain more accurate estimates. We implement a bootstrap application and an asymptotic application. We convert both applications to simulation versions and then implement a simulation study for evaluating the performance of both bootstrap confidence intervals and asymptotic confidence intervals. From the observed coverages, we conclude that bootstrap confidence intervals perform much better than asymptotic confidence intervals for small sample sizes such as n = 21 and for larger sample sizes such as n = 42. These applications and simulation are implemented using S, C, FORTRAN and SAS. In the recommendations for future research, we indicate how our methodology can be extended to more generalized compartmental models. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Statistics." |
| Physical Description: | xii, 89 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |