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We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $theta_1$ in a non-degenerate diffusion coefficient and a parameter $theta_2$ in the drift term. The second component has a drift term parameterized by $theta_3$ and no diffusion term. Asymptotic normality is proved in three different situations for an adaptive estimator for $theta_3$ with some initial estimators for ($theta_1$ , $theta_2$), an adaptive one-step estimator for ($theta_1$ , $theta_2$ , $theta_3$) with some initial estimators for them, and a joint quasi-maximum likelihood estimator for ($theta_1$ , $theta_2$ , $theta_3$) without any initial estimator. Our estimators incorporate information of the increments of both components. Thanks to this construction, the asymptotic variance of the estimators for $theta_1$ is smaller than the standard one based only on the first component. The convergence of the estimators for $theta_3$ is much faster than the other parameters. The resulting asymptotic variance is smaller than that of an estimator only using the increments of the second component.
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on the Golde
In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the estimation of $f(x,.)$ where $x$ is a fixed point. W
We address the problem of adaptive minimax density estimation on $bR^d$ with $bL_p$--loss on the anisotropic Nikolskii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm inde
We aim at estimating the invariant density associated to a stochastic differential equation with jumps in low dimension, which is for $d=1$ and $d=2$. We consider a class of jump diffusion processes whose invariant density belongs to some Holder spac
This paper studies the estimation of the conditional density f (x, $times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $in$ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with typically r d