Minimax results for estimating integrals of analytic processes
Local polynomial estimation of the mean function and its derivatives based on functional data and regular designs
We study the estimation of the mean function of a continuous-time stochastic process and its derivatives. The covariance function of the process is assumed to be nonparametric and to satisfy mild smoothness conditions. Assuming that independent realizations of the process are observed at a sampling design of size generated by a positive density, we derive the asymptotic bias and variance of the local polynomial estimator as increase to infinity. We deduce optimal sampling densities, optimal bandwidths,...
Minimax results for estimating integrals of analytic processes
The problem of predicting integrals of stochastic processes is considered. Linear estimators have been constructed by means of samples at N discrete times for processes having a fixed Hölderian regularity > 0 in quadratic mean. It is known that the rate of convergence of the mean squared error is of order N. In the class of analytic processes , ≥ 1, we show that among all estimators, the linear ones are optimal. Moreover, using optimal coefficient estimators derived...
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