On adaptive minimax density estimation on $$R^d$$ R d

On minimax density estimation on R

the problem of density estimation on R from an independent sample X1, ...XN with common density f is concerned. The behavior of the minimax Lp-risk, 1 ≤ p ≤ ∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is provided. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator...

On Locally Adaptive Density Estimation

In this paper, theoretical and practical aspects of the sample-point adaptive positive kernel density estimator are examined. A closed-form expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact behavior of the optimally adaptive smoothing parameter function is studied for the rst time. The approach d...

Near-minimax recursive density estimation on the binary hypercube

This paper describes a recursive estimation procedure for multivariate binary densities using orthogonal expansions. For d covariates, there are 2 basis coefficients to estimate, which renders conventional approaches computationally prohibitive when d is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time a...

Maxiset for Density Estimation on R

The problem of density estimation on R is considered. Adopting the maxiset point of view, we focus on performance of adaptive procedures. Any rule which consists in neglecting the wavelet empirical coefficients smaller than a sequence of thresholds vn will be called an elitist rule. We prove that for such a procedure the maximal space for the rate v n , with 0 < α < 1, is always contained in th...

Varying kernel density estimation on R+