Maximum Likelihood Methods for Fitting Parametric Statistical Models

Document Type

Article

Publication Date

1-1-1994

Abstract

The likelihood function provides a versatile method for assessing the information that the data contains on parameters or functions of parameters. Specifically, use of the likelihood function provides a generally useful method for finding approximate confidence regions or intervals for the parameters and functions of parameters. This chapter discusses maximum likelihood (ML) methods for fitting parametric statistical models. It focusses on point estimation and the methods of obtaining confidence intervals (for scalars) and confidence regions (for simultaneous inference on a vector of two or more quantities). Confidence intervals and regions quantify the uncertainty in parameter estimates arising from the fact that there are only a finite number of observations from the process or population of interest. Importantly, confidence intervals and regions do not account for possible model misspecification. The chapter also describes “interval-censored” data that arise because of round-off, binning, or when inspections are done at discrete time points in a life test and potential problems by using the “density approximation” for exact observations. It also discusses left-censored observations, right-censored observations, left truncation, right truncation, and method and application to the exponential distribution (a one-parameter model). The approximate confidence regions and intervals based on the asymptotic normality of ML estimators, fitting the Weibull with left-censored observations (a Two- Parameter Model), and fitting the limited failure population model (a three-parameter model) are also discussed in the chapter. © 1994, Academic Press Inc.

Publication Source (Journal or Book title)

Methods in Experimental Physics

First Page

211

Last Page

244

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