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 Free Access
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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 ${\chi ^2}$ tests and a Cramér-von Mises test, based on empirical probability distributions.
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
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
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)
H. T. Banks and B. G. Fitzpatrick, Estimation of growth rate distributions in size structured population models, Quart. Appl. Math. 49, 215–235 (1991)
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)
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA, 1989
P. Billingsley, Probability and Measure, Wiley, New York, 1979
P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968
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)
N. Dunford and J. T. Schwartz, Linear Operators, I: General Theory, Wiley-Interscience, New York, 1958
J. Durbin, Weak convergence of the sample distribution function when parameters are estimated, Ann. Statist. 1, 279–290 (1973)
S. N. Ethier and T. G. Kurtz, Markov Processes : Characterization and Convergence, Wiley, New York, 1986
M. Kendall and A. Stuart, The Advanced Theory of Statistics,vol. 2, 4th ed., Griffin, London, 1979
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
B. L. S. Prakasa Rao, Nonparametric functional estimation, Academic Press, Orlando, FL, 1983
A. N. Schumitzky, Nonparametric EM algorithms for estimating prior distributions, Appl. Math. Comput. 45, 143–157 (1991)
G. R. Shorack and J. A. Wellner, Empirical processes with applications to statistics, Wiley, New York, 1986
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
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
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)
H. T. Banks and B. G. Fitzpatrick, Estimation of growth rate distributions in size structured population models, Quart. Appl. Math. 49, 215–235 (1991)
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)
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA, 1989
P. Billingsley, Probability and Measure, Wiley, New York, 1979
P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968
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)
N. Dunford and J. T. Schwartz, Linear Operators, I: General Theory, Wiley-Interscience, New York, 1958
J. Durbin, Weak convergence of the sample distribution function when parameters are estimated, Ann. Statist. 1, 279–290 (1973)
S. N. Ethier and T. G. Kurtz, Markov Processes : Characterization and Convergence, Wiley, New York, 1986
M. Kendall and A. Stuart, The Advanced Theory of Statistics,vol. 2, 4th ed., Griffin, London, 1979
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
B. L. S. Prakasa Rao, Nonparametric functional estimation, Academic Press, Orlando, FL, 1983
A. N. Schumitzky, Nonparametric EM algorithms for estimating prior distributions, Appl. Math. Comput. 45, 143–157 (1991)
G. R. Shorack and J. A. Wellner, Empirical processes with applications to statistics, Wiley, New York, 1986
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Article copyright:
© Copyright 1995
American Mathematical Society
