Statistical tests of fit in estimation problems for structured population modeling

Author:
Ben G. Fitzpatrick

Journal:
Quart. Appl. Math. **53** (1995), 105-128

MSC:
Primary 62E20; Secondary 62G10, 62P10

DOI:
https://doi.org/10.1090/qam/1315451

MathSciNet review:
MR1315451

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We present a statistical model of the type of data used in many applications of least squares estimation techniques to structured population problems. By viewing the data as a random sample from the size density, we may apply various statistical goodness of fit tests assess dynamic models for the data. We examine in particular classical tests and a Cramér-von Mises test, based on empirical probability distributions.

**[Ba]**H. T. Banks,*On a variational approach to some parameter estimation problems*, Distributed Parameter Systems, Lecture Notes in Control and Information Sciences, vol. 75 (F. Kappel, K. Kunisch, and W. Schappacher, eds.), Springer-Verlag, Berlin, 1985, pp. 1-23**[BBKW1]**H. T. Banks, L. Botsford, F. Kappel, and C. Wang,*Modeling and estimation in size structured population models*, Mathematical Ecology (Proc., Trieste, 1986), World Sci. Publ., Singapore, 1988, pp. 521-541**[BBKW2]**H. T. Banks, L. Botsford, F. Kappel, and C. Wang,*Estimation of growth and survival in size-structured cohort data: An application to larval striped bass (Morone Saxatilis)*, J. Math. Biology**30**, 125-150 (1991)**[BF1]**H. T. Banks and B. G. Fitzpatrick,*Estimation of growth rate distributions in size structured population models*, Quart. Appl. Math.**49**, 215-235 (1991)**[BF2]**H. T. Banks and B. G. Fitzpatrick,*Statistical tests for model comparison in parameter estimation problems for distributed parameter systems*, J. Math. Biology**28**, 501-527 (1990)**[BK]**H. T. Banks and K. Kunisch,*Estimation Techniques for Distributed Parameter Systems*, Birkhäuser, Boston, MA, 1989**[Bi1]**P. Billingsley,*Probability and Measure*, Wiley, New York, 1979**[Bi2]**P. Billingsley,*Convergence of Probability Measures*, Wiley, New York, 1968**[BVWLKRC]**L. Botsford, B. Vandracek, T. Wainwright, A. Linden, R. Kope, D. Reed, and J. J. Cech,*Population development of the mosquitofish, Gambusia Affinis, in rice fields*, Environmental Biology of Fishes**20**, 143-154 (1987)**[B]**N. Dunford and J. T. Schwartz,*Linear Operators*, I:*General Theory*, Wiley-Interscience, New York, 1958**[D]**J. Durbin,*Weak convergence of the sample distribution function when parameters are estimated*, Ann. Statist.**1**, 279-290 (1973)**[EK]**S. N. Ethier and T. G. Kurtz,*Markov Processes : Characterization and Convergence*, Wiley, New York, 1986**[KS]**M. Kendall and A. Stuart,*The Advanced Theory of Statistics*,vol. 2, 4th ed., Griffin, London, 1979**[L]**A. F. Low, 1986*Striped bass egg and larva survey in the Sacramento-San Joaquin Estuary*, California Department of Fish and Game, Sacramento, CA, 1986**[PR]**B. L. S. Prakasa Rao,*Nonparametric functional estimation*, Academic Press, Orlando, FL, 1983**[S]**A. N. Schumitzky,*Nonparametric EM algorithms for estimating prior distributions*, Appl. Math. Comput.**45**, 143-157 (1991)**[SW]**G. R. Shorack and J. A. Wellner,*Empirical processes with applications to statistics*, Wiley, New York, 1986

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
62E20,
62G10,
62P10

Retrieve articles in all journals with MSC: 62E20, 62G10, 62P10

Additional Information

DOI:
https://doi.org/10.1090/qam/1315451

Article copyright:
© Copyright 1995
American Mathematical Society