Non parametric optimal estimation of the regression function

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One main function of statistical science is to demonstrate how valid inferences about some population may be made from an examination of the information provided by a sample or a set of a given data. To achieve this, an appropriate model exhibiting parsimony of parameters with a well-defined scope has to be selected. Once the desired model has been identified, there is a need to obtain precise estimate of all the parameters of the model before it is fitted. The problem of estimation is how to achieve the precision of the estimates. This can better be addressed by having an insight into approaches to estimation. The main approaches to estimation are parametric and non-parametric. In this project, proposed how to choose the weights such that the efficiency of the estimation is improved. We replaced the weights with the empirically estimated covariances. The non-parametrically estimated variance function will approximate the true variance function. Therefore, the estimating equations with the estimated variance function are expected to achieve the optimality in estimating the regression co-efficient in the absence of any knowledge regarding the true variance function.