Linear Statistical Calibration

Much has been said about the classical and the inverse methods of calibration for the univariate and to some extent about the multivariate case also in the existing literature, see Brown(1982). We have explored the possibilities of using the best linear predictor both in the univariate and the multivariate situations. First four chapters deal mainly with the univariate case, chapters five and six deal with the multivariate situation and chapter seven is devoted to the Bayesian version of best linear predictor. First chapter introduces calibration and discusses different methods of calibration in the univariate situation. Chapter 2 gives a review of the calibration literature for classical, Bayesian and best linear predictor approaches with some comments. Chapter 3 deals with the derivation of the best linear predictor and approximates its unconditional mean squared error by Taylor's series. A simulation study is made to compare the approximated and the simulated values. Chapter 4 starts with the interval estimates and possible aims. Two situations with the known and unknown parameters are studied. Tail probabilities are calculated for different P(t). Chapter 5 introduces multivariate calibration and reviews the literature. Much attention is focussed on the case when there are q response variables and there is only one explanatory variable p i.e. general q and p = 1. Best linear predictor is derived and its mean squared error in canonical form is studied by simulation. In chapter 6 approximation to mean squared error is obtained by regressing simulated data and the interval estimates are studied. Chapter 7 gives a Bayesian treatment of the best linear predictor both in the univariate and the multivariate case