‘An unusual family, US. There’s Dad, who isn’t here but whose shadow is, Mum who is here but whose heart is broken. There’s Gina who’s sad and Karen who’s not. There’s Victor who’s intelligent and me who isn’t. There was Adam too, who hurt us more than we imagined we could be hurt …’ Us deals with a family’s struggle to survive…
The fourth chapter is an introduction to asymptotic methods of estimation. The method of statistical moments and the maximum-likelihood method are investigated.The sufficient conditions for asymptotical normality of the estimators are given for both methods.The linear and quadratic methods of estimation are dealt with in the fifth chapter.The method of least squares estimation is treated.Five basic regular versions of the regression model and the unified linear model of estimation are described. Unbiased estimators for unit dispersion (factor of the covariance matrix) are given for all mentioned cases.The equivalence of the least-squares method to the method of generalized minimum norm inversion of the design matrix of the regression model is studied in detail.The problem of estimating the covariance components in the mixed model is mentioned as well.Statistical properties of linear and quadratic estimators developed in the fifth chapter in the case of normally distributed errors of measurement are given in Chapter 6.Further, the application of tensor products of Hilbert spaces generated by the covariance matrix of random error vector of observations is demonstrated.Chapter 7 reviews some further important methods of estimation theory. In the first part Wald's method of decision functions is applied to the construction of estimators.The method of contracted estimators and the method of Hoerl and Kennard are presented in the second part. The basic ideas of robustness and Bahadur's approach to estimation theory are presented in the third and fourth parts of this last chapter.