Identification of stochastic nonlinear models using optimal estimating functions

This chapter covers multiple regression and links statistical inference to general topics such as lurking variables that arose earlier. Many examples can be used to illustrate multiple regression, but we have found it useful to come to class prepared with a specific example, with computer output (since our students learn to run the regressions on the computer). We have found it is a good strategy to simply use a regression analysis from some published source (e.g., a social science journal) and go through the model and its interpretation with the class, asking students how the regression results would have to differ in order for the study’s conclusions to change. The chapter includes examples that revisit the simple linear model of height and income, involve the class in models of exam scores, and fit a nonlinear model (for more advanced classes) for golf putting.

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Set-membership identifiability of nonlinear models and related parameter estimation properties

International Journal of Applied Mathematics and Computer Science ◽

10.1515/amcs-2016-0057 ◽

2016 ◽

Vol 26 (4) ◽

pp. 803-813 ◽

Cited By ~ 2

Author(s):

Carine Jauberthie ◽

Louise Travé-MassuyèEs ◽

Nathalie Verdière

Keyword(s):

Mathematical Model ◽

Parameter Estimation ◽

Dynamic System ◽

Nonlinear Models ◽

Differential Algebra ◽

Related Parameter ◽

Set Membership ◽

Estimation Problems ◽

The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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