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We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
A general method to combine several estimators of the same quantity is investigated. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained…
In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk's classical isotonic estimator. We also…
This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…
In this paper the method of simulated quantiles (MSQ) of Dominicy and Veredas (2013) and Dominick et al. (2013) is extended to a general multivariate framework (MMSQ) and to provide a sparse estimator of the scale matrix (sparse-MMSQ). The…
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…
We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…
The subject of robust estimation in time series is widely discussed in literature. One of the approaches is to use GM-estimation. This method incorporates a broad class of nonparametric estimators which under suitable conditions includes…
We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing…
Suppose that the normal model is used for data $Y_1,\ldots,Y_n$, but that the true distribution is a t-distribution with location and scale parameters $\xi$ and $\sigma$ and $m$ degrees of freedom. The normal model corresponds to…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
For a given parametric probability model, we consider the risk of the maximum likelihood estimator with respect to $\alpha$-divergence, which includes the special cases of Kullback--Leibler divergence, the Hellinger distance and $\chi^2$…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…