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Vol 28, No 3 (2019)
- Year: 2019
- Articles: 3
- URL: https://journal-vniispk.ru/1066-5307/issue/view/13911
Article
Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences
Abstract
In this paper we are concerned with the weak convergence to Gaussian processes of conditional empirical processes and conditional U-processes from stationary β-mixing sequences indexed by classes of functions satisfying some entropy conditions. We obtain uniform central limit theorems for conditional empirical processes and conditional U-processes when the classes of functions are uniformly bounded or unbounded with envelope functions satisfying some moment conditions. We apply our results to introduce statistical tests for conditional independence that are multivariate conditional versions of the Kendall statistics.
169-207
Density Deconvolution with Small Berkson Errors
Abstract
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some cases, the unknown density estimator can be obtained by simple averaging without using kernels. However, this may not be the case when Berkson errors are asymptotically small. By treating the former case as a kernel estimator with the zero bandwidth, we obtain the optimal expressions for the bandwidth. We show that the density of Berkson errors acts as a regularizer, so that the kernel estimator is unnecessary when the variance of Berkson errors lies above some threshold that depends on the shapes of the densities in the model and the number of observations.
208-227
Maxiset Point of View for Signal Detection in Inverse Problems
Abstract
This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robust version of these maxisets allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct and indirect testing procedures.
228-242