This paper deals with semiparametric convolution models, where the noise sequence has a gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal’s density...
This paper deals with semiparametric convolution models, where the
noise sequence has a Gaussian centered distribution, with unknown
variance. Non-parametric convolution models are concerned with the case of an
entirely known distribution for the noise sequence, and they have
been widely studied in the past decade. The main property of those
models is the following one: the more regular the distribution of the
noise is, the worst the rate of convergence for the estimation of the
signal's density...
This paper deals with order identification for Markov chains with Markov
regime (MCMR) in the context of finite alphabets. We define the joint order
of a MCMR process in terms of the number of states of the hidden Markov
chain and the memory of the conditional Markov chain. We study the
properties of penalized maximum likelihood estimators for the unknown order
of an observed MCMR process, relying on information theoretic
arguments. The novelty of our work relies in the joint 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 -values under the null hypothesis and the other component 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 in the mixture, relying on a preliminary estimator of the unknown...
In a convolution model, we observe random variables whose distribution is the convolution of some unknown density and some known noise density . We assume that is polynomially smooth. We provide goodness-of-fit testing procedures for the test
: =
, where the alternative
is expressed with respect to -norm (i.e. has the form ). Our procedure is adaptive with respect to the unknown smoothness parameter of . Different testing rates (
...
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