Hypothesis Tests and Confidence Intervals or Regions

This chapter demonstrates how R and SAS can be used to perform hypothesis tests and to construct confidence intervals or regions. Inference is demonstrated using the large-sample approximate normality of maximum likelihood estimators (MLEs) (the Wald approach), and using the approximate χ2 distribution of likelihood ratio statistics. Hypothesis tests and confidence intervals/regions are considered for a single element θk of the parameter vector, θ, and for a subset of (or all) elements of θ. There is undeniable virtue in the simplicity of the Wald approach, and in many cases it will make little difference compared to using the likelihood ratio. To encourage use of the likelihood ratio, the chapter includes demonstration of the R function Plkhci and SAS macro of the same name for construction of likelihood ratio confidence intervals. Controlled Vocabulary Terms confidence interval; hypothesis testing; likelihood ratio test; maximum likelihood estimator; profile likelihood; Wald test