In the preceding chapter we considered different predictors in models at which the mean value of X(.) was unknown and modeled by some regression models. The main assumption under which these predictors were derived was that the covariance characteristics of the models were known. This is a rather strong assumption which is fulfilled only rarely in practical problems when we have usually only time series data x consisting of a finite realization of an observation X of X(.) and nothing more. Thus it is necessary to model not only the mean value m(.) of X(.), but also the covariance function R(.,.) of X(.). The main models for covariance functions were considered in the preceding chapter and also the methods, giving the estimators, such as the DOOLSE, the DOWELSE, and the MLE, of parameters of covariance functions were derived.
KeywordsCovariance Function Concave Function Weighted Residual Multivariate Normal Distribution Asymptotic Covariance Matrix
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