共查询到6条相似文献,搜索用时 93 毫秒
1.
In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise
(standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees
of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances
of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain
how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty
term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known
or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising
and of compression. 相似文献
2.
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved.
Received: 28 August 1998 / Revised version: 6 September 1999 / Published online: 14 June 2000 相似文献
3.
D. Fourdrinier S. Pergamenshchikov 《Annals of the Institute of Statistical Mathematics》2007,59(3):435-464
This paper is devoted to nonparametric estimation, through the
-risk, of a regression function based on observations with spherically symmetric errors, which are dependent random variables
(except in the normal case). We apply a model selection approach using improved estimates. In a nonasymptotic setting, an
upper bound for the risk is obtained (oracle inequality). Moreover asymptotic properties are given, such as upper and lower
bounds for the risk, which provide optimal rate of convergence for penalized estimators. 相似文献
4.
《Stochastic Processes and their Applications》2015,125(1):294-326
The paper considers the problem of estimating a periodic function in a continuous time regression model observed under a general semimartingale noise with an unknown distribution in the case when continuous observation cannot be provided and only discrete time measurements are available. Two specific types of noises are studied in detail: a non-Gaussian Ornstein–Uhlenbeck process and a time-varying linear combination of a Brownian motion and compound Poisson process. We develop new analytical tools to treat the adaptive estimation problems from discrete data. A lower bound for the frequency sampling, needed for the efficiency of the procedure constructed by discrete observations, has been found. Sharp non-asymptotic oracle inequalities for the robust quadratic risk have been derived. New convergence rates for the efficient procedures have been obtained. An example of the regression with a martingale noise exhibits that the minimax robust convergence rate may be both higher or lower as compared with the minimax rate for the “white noise” model. The results of Monte-Carlo simulations are given. 相似文献
5.
Xia Chen 《Probability Theory and Related Fields》2000,116(1):89-123
Let {X
n
}
n
≥0 be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals
of the form
where ƒ is a real π-centered function defined on E. Some similar results are also obtained for additive functionals which are martingales associated with {X
n
}
n
≥0.
Received: 15 September 1998 / Revised version: 1 April 1999 相似文献
6.
Harro Walk 《Annals of the Institute of Statistical Mathematics》2005,57(4):665-685
The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable.
For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL
2-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for
Cesàro summability. 相似文献