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We study semiparametric inference in some linear regression models with time-varying coefficients, dependent regressors and dependent errors. This problem, which has been considered recently by Zhang and Wu (2012) under the functional…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
In this article, variational state estimation is examined from the dynamic programming perspective. This leads to two different value functional recursions depending on whether backward or forward dynamic programming is employed. The result…
Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its $k$-dimensional projection $\mathbf{a}_{n,k}X^{(n)}$, where $\mathbf{a}_{n,k}$ is an $n \times k$-dimensional matrix belonging to the Stiefel manifold…
We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection…
We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in…
We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…
We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the…
We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary,…
Let $X_1,..., X_n \in \mathbb{R}^d$ be independent Gaussian random vectors with independent entries and variance profile $(b_{ij})_{i \in [d],j \in [n]}$. A major question in the study of covariance estimation is to give precise control on…
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
It is tempting to evaluate F2(x,1) and similar univariate specializations of Appell's functions by evaluating the apparent power series at x=0 straight away using the Gauss formula for 2F1(1). But this kind of naive evaluation can lead to…
In this paper, we consider directly estimating the eigenvalues of precision matrix, without inverting the corresponding estimator for the eigenvalues of covariance matrix. We focus on a general asymptotic regime, i.e., the large dimensional…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
This paper is devoted to the study of large deviation behaviors in the setting of the estimation of the regression function on functional data. A large deviation principle is stated for a process Zn, defined below, allowing to derive a…
We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian…
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…