Mean square error for histograms when estimating Radon-Nikodym derivatives.
Mean square error of the estimator of the conditional hazard function
This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
We observe an infinitely dimensional Gaussian random vector x = ξ + v where ξ is a sequence of standard Gaussian variables and v ∈ l2 is an unknown mean. We consider the hypothesis testing problem H0 : v = 0versus alternatives for the sets . The sets Vε are lq-ellipsoids of semi-axes ai = i-s R/ε with lp-ellipsoid of semi-axes bi = i-r pε/ε removed or similar Besov bodies Bq,t;s (R/ε) with Besov bodies Bp,h;r (pε/ε) removed. Here or are the parameters which define the sets Vε for given radii...
Minimum Distance Estimation of the Center of Symmetry with Randomly Censored Data.
min-wise independent linear permutations.
Model and variable selection procedures for semiparametric time series regression.
Modelos GARCH e TARCH - estacionaridade forte, estacionaridade fraca, ergodicidade e comportamento limite do agregado temporal
Nearest neighbor classification in infinite dimension
Let X be a random element in a metric space (F,d), and let Y be a random variable with value 0 or 1. Y is called the class, or the label, of X. Let (Xi,Yi)1 ≤ i ≤ n be an observed i.i.d. sample having the same law as (X,Y). The problem of classification is to predict the label of a new random element X. The k-nearest neighbor classifier is the simple following rule: look at the k nearest neighbors of X in the trial sample and choose 0 or 1 for its label according to the majority vote. When , Stone...
Necessary conditions for the bootstrap of the mean of a triangular array
New M-estimators in semi-parametric regression with errors in variables
In the regression model with errors in variables, we observe n i.i.d. copies of (Y, Z) satisfying Y=fθ0(X)+ξ and Z=X+ɛ involving independent and unobserved random variables X, ξ, ɛ plus a regression function fθ0, known up to a finite dimensional θ0. The common densities of the Xi’s and of the ξi’s are unknown, whereas the distribution of ɛ is completely known. We aim at estimating the parameter θ0 by using the observations (Y1, Z1), …, (Yn, Zn). We propose an estimation procedure based on the least...
New variance ratio tests to identify random walk from the general mean reversion model.
Nonparametric adaptive estimation for pure jump Lévy processes
This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at n discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive estimator....
Nonparametric Curve Estimation with Bernstein Estimates.
Nonparametric density estimators based on nonstationary absolutely regular random sequences.
Nonparametric estimation of probability density functions based on orthogonal expansions.
Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation
In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of p-values under the null hypothesis and the other component f is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component f in the mixture, relying on a preliminary estimator of the...
Nonparametric estimation of the ratios of derivatives of a multivariate distribution density from dependent observations.
Nonparametric inference for discretely sampled Lévy processes
Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.
Nonparametric Maximum Likelihood Estimation in a Non Locally Compact Setting.