Related papers: Information Geometry and Asymptotics for Kronecker…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…
We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in this work is a striking resonant interaction between…
The extremal dependence structure of a regularly varying $d$-dimensional random vector can be described by its angular measure. The standard nonparametric estimator of this measure is the empirical measure of the observed angles of the $k$…
The counting of the dimension of the space of $U(N) \times U(N) \times U(N)$ polynomial invariants of a complex $3$-index tensor as a function of degree $n$ is known in terms of a sum of squares of Kronecker coefficients. For $n \le N$, the…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
Thomas' partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox's model. This paper proposes a new estimator of the regression parameters, which is consistent and…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
An additive growth curve model with orthogonal design matrices is proposed in which observations may have different profile forms. The proposed model allows us to fit data and then estimate parameters in a more parsimonious way than the…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…
Kronecker PCA involves the use of a space vs. time Kronecker product decomposition to estimate spatio-temporal covariances. In this work the addition of a sparse correction factor is considered, which corresponds to a model of the…
The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…
We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…