ABSTRACT
This chapter summarises the statistical aspects of Lp-norm estimators. It deals with statistical inference, the statistical properties of the estimator θ^ of the true parameter vector θ and finally critique of the model f(x, θ). R. Koenker and G. Bassett investigated three test statistics viz: the Wald, pseudo-likelihood ratio and Lagrange multiplier tests. The logical step after parameter estimation and inference is critique of the model. This involves the use of regression diagnostics to detect outliers and identify influential observations. For the linear model, Bassett and R. Koenker and H. Nyquist derived the asymptotic distribution of the L1-norm estimator. The general jackknife approach seems to be related to the bias reduction technique of Quenouille. Goodness-of-fit tests use statistics based on the observed empirical distribution function (EDF) of the data. EDF statistics are discussed by M. A. Stephens.
