Adaptivity and optimality of the monotone least squares estimator
نویسنده
چکیده
In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained rate is given by a functional relation using the underlying function f0, and not by some smoothness parameter, and that this rate is optimal when considering the class of all monotone functions, in the sense that there exists a sequence of alternative monotone functions f1, such that no other estimator can attain a better rate for both f0 and f1. We also show that under mild conditions the estimator attains the same rate in L sense, and we give general conditions for which we can calculate a (non-standard) limiting distribution for the estimator.
منابع مشابه
Technical report : Adaptivity and optimality of the monotone least squares estimator for four different models
In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained rate is given by a functional relation using the underlying function f 0 , and not by some smoothness parameter, and that this rate is optimal when considering ...
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