Abstract
This chapter discusses methods for the estimation of functionals related to density. These methods can be used for the estimation of regression functions, failure rates, derivatives of densities, and ratio of densities. One of these methods presented in the chapter involves the estimation of f(p) by the pth-order derivative of the kernel estimator of f for a suitable kernel K(·). Several methods of estimation are known. The chapter presents a study of the asymptotic distribution of the estimator of the integral regression function as the number of observation points becomes infinite. The notion of failure rate in the multidimensional case has been extended in several directions. Either a scalar-valued multivariate failure rate or a vector-valued multivariate failure rate, which is also called the hazard gradient, can be used in the evaluation of the performance of a multidimensional variate. At times, the problem of interest is estimation of density in the presence of noise.
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