Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice

Vladimir Spokoiny
New method of adaptive estimation of a regression function is proposed. The resulting estimator achieves near optimal rate of estimation in the classical sense of mean integrated squared error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function ƒ or its derivatives. For instance, in the case of a jump of a regression function, beyond the interval of length (in order) n-1 log n...
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