# Parameter Estimation Methods

## Abstract

This chapter covers topics related to estimation of model parameters and to model identification of univariate and multivariate problems not covered in earlier chapters. First, the fundamental notion of estimability of a model is introduced which includes both structural and numerical identifiability concepts. Recall that in Chap. 5 issues addressed were relevant to parameter estimation of linear models and to variable selection using step-wise regression in multivariate analysis. This chapter extends these basic notions by presenting the general statistical parameter estimation problem, and then presenting a few important estimation methods. Multivariate estimation methods (such as principle component analysis, ridge regression and stagewise regression) are discussed along with case study examples. Next, the error in variable (EIV) situation is treated when the errors in the regressor variables are large. Subsequently, another powerful and widely used estimation method, namely maximum likelihood estimation (MLE) is described, and its application to parameter estimation of probability functions and logistic models is presented. Also covered is parameter estimation of models non-linear in the parameters which can be separated into those that are transformable into linear ones, and those which are intrinsically non-linear. Finally, computer intensive numerical methods are discussed since such methods are being increasingly used nowadays because of the flexibility and robustness they provide. Different robust regression methods, whereby the influence of outliers on parameter estimation can be deemphasized, are discussed. This is, followed by the bootstrap resampling approach which is applicable for parameter estimation, and for ascertaining confidence limits of estimated model parameters and of model predictions.

## Keywords

Partial Little Square Principle Component Analysis Ridge Regression Regressor Variable Structural Identifiability## Supplementary material

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