Estimation Theory for the Cusp Catastrophe Model

Cobb, Loren (1980): Estimation Theory for the Cusp Catastrophe Model. Published in: Proceedings of the American Statistical Association, Section on Survey Research Methods (March 1981): pp. 772-776.

Abstract

The cusp model of catastrophe theory is very closely related to certain multiparameter exponential families of probability density functions. This relationship is exploited to create an estimation theory for the cusp model. An example is presented in which an independent variable has a bifurcation effect on the dependent variable.

• Item Type: MPRA Paper
• Language: English
• Keywords: cusp, catastrophe, exponential family
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General

References

Cobb, Loren (1978) “Stochastic catastrophe models and multimodal distributions,” Behavioral Science, v. 23, 360–374.

Cobb, Loren (1980) “Stochastic differential equations for the social sciences,” Chapter 2 in Mathematical Frontiers of the Social and Policy Sciences, edited by Loren Cobb and R. M. Thrall. Boulder, CO: Westview Press.

Cobb, Loren and Watson, William B. (1981) “Statistical catastrophe theory: An overview,” Mathematical Modeling, v. 1, 311–317.

Drew, G. C., Colquhoun, W.P., and Long, H.A. (1959) “Effect of small doses of alcohol on a skill resembling driving,” Memo 38. London: Medical Research Council.

Ferdon, Marybeth E. (1983) Inference for Quadratic and Catastrophe Response Surface Models. Unpublished doctoral dissertation. Charleston, SC: Department of Biostatistics and Epidemiology, Medical University of South Carolina.

Grasman, Raoul P., van der Maas, Han L., and Wagenmakers, Eric-Jan (2009) “Fitting the cusp catastrophe in R: A cusp package primer,” Journal of Statistical Software, vol. 32, #8, 1–27.

Lehman, E.L. (1959) Testing Statistical Hypotheses. New York: Wiley.

Poston, Timothy and Stewart, Ian (1978) Catastrophe Theory and Its Applications. London: Pitman.

Sussmann, H.J. and Zahler, R.S. (1978) “A critique of applied catastrophe theory in the behavioral sciences,” Behavioral Science, vol. 23, 383–389.

Thom, René (1975) Structural Stability and Morphogenesis. Reading, MA: Benjamin.

Zeeman, E. Christopher (1977) Catastrophe Theory: Selected Papers. Reading, MA: Addison-Wesley.