Related papers: Moderate deviations for a nonparametric estimator …

In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a…

Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of…

Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…

This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…

The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…

We consider robust location-scale estimators under contamination. We show that commonly used robust estimators such as the median and the Huber estimator are inconsistent under asymmetric contamination, while the Tukey estimator is…

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…

We study the Cram\'er type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric…

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

We study the problem of nonparametric estimation of the fractional derivative of unknown distribution function and of spectral function and show that these problems are well posed when the order of derivative is less than 0.5. We prove also…

This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…

In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed…

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…

We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points…

We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…

Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence…