Maximum Likelihood Estimation of Functional Relationships

1:Introduction.- I.Introduction.- II.Inference.- III.Controlled variables.- IV.Outline of the following chapters.- 2:Maximum likelihood estimation of functional relationships.- I.Introduction.- II.Maximization of the likelihood under constraints.- A.Direct elimination.- B.The Lagrange multiplier method.- III.The conditional likelihood.- IV.Maximum likelihood estimation for multivariate normal distributions with known covariance matrix.- A.Derivation of the normal equations.- B.The simple linear functional relationship.- C.Estimation using Sprent's generalized residuals.- D.Non-linear models.- E.Inconsistency of non-linear ML estimators.- F.Linearization of the normal equations.- V.Maximum likelihood estimation for multivariate normal distributions with unknown covariance matrix.- A.Estimation with replicated observations.- B.Estimation without replicated observations.- C.A saddlepoint solution to the normal equations.- VI.Covariance matrix of estimators.- A.The asymptotic method.- B.The bootstrap.- C.The jackknife.- VII.Error distributions depending on the true variables.- VIII.Proportion of explained variation.- 3:The multivariate linear functional relationship.- I.Introduction.- II.Identifiability.- III.Heteroscedastic errors.- A.Known error covariance matrix.- B.Unknown error covariance matrix.- IV.Homoscedastic errors.- A.Known error covariance matrix.- B.Misspecification.- C.The eigenvalue method.- D.Unknown error covariance matrix.- V.Factor space.- VI.The asymptotic distribution of the parameter estimators.- A.Asymptotic covariance matrix.- B.Consistency and asymptotic normality.- C.Hypothesis tests.- VII.Replicated observations.- VIII.Instrumental variables.- References.