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We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance--covariance matrix. Specifically, we introduce a new distribution called the truncated…
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…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…
This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…
In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error…