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Найдено 9 публикаций
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Статья
Le Gouic T., Paris Q. Electronic journal of statistics. 2018. Vol. 12. No. 2. P. 4239-4263.
Добавлено: 9 ноября 2018
Статья
Silin I., Spokoiny V. Electronic journal of statistics. 2018. Vol. 12. No. 1. P. 1948-1987.
Добавлено: 23 июля 2018
Статья
Belomestny D., Panov V. Electronic journal of statistics. 2013. Vol. 7. P. 2970-3003.
Добавлено: 23 сентября 2013
Статья
Lee E., Mammen E. Electronic journal of statistics. 2016. Vol. 10. No. 1. P. 855-894.

Varying coefficient models are useful generalizations of parametric linear models. They allow for parameters that depend on a covariate or that develop in time. They have a wide range of applications in time series analysis and regression. In time series analysis they have turned out to be a powerful approach to infer on behavioral and structural changes over time. In this paper, we are concerned with high dimensional varying coefficient models including the time varying coefficient model. Most studies in high dimensional nonparametric models treat penalization of series estimators. On the other side, kernel smoothing is a well established, well understood and successful approach in nonparametric estimation, in particular in the time varying coefficient model. But not much has been done for kernel smoothing in high-dimensional models. In this paper we will close this gap and we develop a penalized kernel smoothing approach for sparse high-dimensional models. The proposed estimators make use of a novel penalization scheme working with kernel smoothing. We establish a general and systematic theoretical analysis in high dimensions. This complements recent alternative approaches that are based on basis approximations and that allow more direct arguments to carry over insights from high-dimensional linear models. Furthermore, we develop theory not only for regression with independent observations but also for local stationary time series in high-dimensional sparse varying coefficient models. The development of theory for local stationary processes in a high-dimensional setting creates technical challenges. We also address issues of numerical implementation and of data adaptive selection of tuning parameters for penalization.The finite sample performance of the proposed methods is studied by simulations and it is illustrated by an empirical analysis of NASDAQ composite index data.

Добавлено: 3 июня 2016
Статья
Mammen E., Lee E. Electronic journal of statistics. 2016. Vol. 10. No. 1. P. 855-894.
Добавлено: 12 октября 2016
Статья
Moulines E., Brosse N., Durmus A. Electronic journal of statistics. 2018. Vol. 12. No. 1. P. 851-889.
Добавлено: 12 декабря 2018
Статья
Bellec P., Dalalyan A., Grappin E. et al. Electronic journal of statistics. 2018. Vol. 12. No. 2. P. 3443-3472.
Добавлено: 9 ноября 2018
Статья
Krymova E. A., Chernousova E., Golubev Y. Electronic journal of statistics. 2013. Vol. 7. P. 2395-2419.

Научная статья

Добавлено: 22 августа 2016
Статья
Belomestny D., Panov V. Electronic journal of statistics. 2015. Vol. 9. No. 2. P. 1974-2006.

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type

\[

X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right),

\]

where \(\xi_s\) is a L{\'e}vy process. Our primal goal is to estimate the characteristics of the L\'evy process \(\xi\) from the low-frequency observations of the process \(X\). We present a novel approach towards estimating the L{\'e}vy triplet of \(\xi,\) which is based on the Mellin transform technique. It is shown that the resulting estimates attain optimal minimax convergence rates. The suggested algorithms are illustrated by numerical simulations.

Добавлено: 1 сентября 2015