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Of all publications in the section: 6
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Article
Lee Y., Mammen E., Nielsen J. et al. Annals of Statistics. 2015. No. 43. P. 620-645.

This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed. Identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation. In this paper, the structural assumption is made that the density is a product of one-dimensional functions. The theory is quite general in assuming the shape of the region where the density is observed. Such models naturally arise when the time point of an observation can be written as the sum of two terms (e.g., onset and incubation period of a disease). The developed theory also allows for a multiplicative factor of seasonal effects. Seasonal effects are present in many actuarial, biostatistical, econometric and statistical studies. Smoothing estimators are proposed that are based on backfitting. Full asymptotic theory is derived for them. A practical example from the insurance business is given producing a within year budget of reported insurance claims. A small sample study supports the theoretical results

Added: Dec 12, 2014
Article
Spokoiny V., Zhilova M. Annals of Statistics. 2015. Vol. 43. No. 6. P. 2653-2675.

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension pp: the bootstrap approximation works if p3/np3/n  is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called small modelling bias condition. In the case when the true model deviates significantly from the considered parametric family, the bootstrap procedure is still applicable but it becomes a bit conservative: the size of the constructed confidence sets is increased by the modelling bias. We illustrate the results with numerical examples for misspecified linear and logistic regressions.

Added: Jul 21, 2016
Article
Belomestny D., Goldenshluger A. Annals of Statistics. 2020.

In  this paper we study   the problem

of density deconvolution under general assumptions on the measurement error distribution. Typically

deconvolution estimators are constructed using Fourier transform techniques, and

it is assumed that

the  characteristic function of

the measurement errors does not have zeros

on the real line. This assumption is rather strong and is not fulfilled

in many cases of interest.  In this paper we develop a

methodology for constructing optimal density deconvolution estimators in the general setting that covers

vanishing  and non--vanishing  characteristic functions of the measurement errors.

We derive upper bounds on the risk of the proposed estimators and

provide  sufficient conditions under which zeros of the corresponding characteristic function have no effect on estimation accuracy.

Moreover, we show that the  derived conditions are also necessary in some

specific problem instances.

Added: Apr 7, 2020
Article
Bobkov S. Annals of Statistics. 2019. Vol. 47. No. 3. P. 1616-1633.

Let F_n denote the distribution function of the normalized sum of ni.i.d. random variables. In this paper, polynomial rates of approx- imation of Fn by the corrected normal laws are considered in the model where the underlying distribution has a convolution structure. As a basic tool, the convergence part of Khinchine’s theorem in met- ric theory of Diophantine approximations is extended to the class of product characteristic functions.

Added: Oct 19, 2018
Article
Dalalyan A., Grappin E., Paris Q. Annals of Statistics. 2018. Vol. 46. No. 5. P. 2452-2478.

 

In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is reasonable to use the Laplace distribution as a prior. The resulting estimator and, specifically, a particular instance of it referred to as the Bayesian lasso, was already used in the statistical literature because of its computational convenience, even though no thorough mathematical analysis of its statistical properties was carried out. The present work fills this gap by establishing sharp oracle inequalities for the EWA with the Laplace prior. These inequalities show that if the temperature parameter is small, the EWA with the Laplace prior satisfies the same type of oracle inequality as the lasso estimator does, as long as the quality of estimation is measured by the prediction loss. Extensions of the proposed methodology to the problem of prediction with low-rank matrices are considered.

Added: Nov 26, 2016
Article
Mammen E., Lee Y., Nielsen J. et al. Annals of Statistics. 2016.

In this paper we consider a new structural model for in-sample density forecasting. In-sample density forecasting is to estimate a structured density on a region where data are observed and then re-use the estimated structured density on some region where data are not observed. Our structural assumption is that the density is a product of one-dimensional functions with one function sitting on the scale of a transformed space of observations. The transformation involves another unknown one-dimensional function, so that our model is formulated via a known smooth function of three underlying unknown one-dimensional functions. We present an innovative way of estimating the one-dimensional functions and show that all the estimators of the three components achieve the optimal one-dimensional rate of convergence. We illustrate how one can use our approach by analyzing a real dataset, and also verify the tractable finite sample performance of the method via a simulation study.

Added: Oct 12, 2016