Related papers: Local Quadratic Spectral and Covariance Matrix Est…
The paper deals with the problem of estimating the M$^2$ (i.e. multivariate and multidimensional) spectral density function of a stationary random process or random field. We propose the $f$-truncated periodogram, i.e. a truncated…
Improving the efficiency of discrete time scale invariant (DSI) processes, we consider some flexible sampling of a continuous time DSI process ${X(t), t\in{R^+}}$ with scale $l>1$, which is in correspondence to some multi-dimensional…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…
We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…
Many simulation problems require the estimation of a ratio of two expectations. In recent years Monte Carlo estimators have been proposed that can estimate such ratios without bias. We investigate the theoretical properties of such…
In light of WMAP results, we examine the observational constraint on the P-term inflation. With the tunable parameter $f$, P-term inflation contains richer physics than D-term and F-term inflationary models. We find the logarithmic…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…
Consider a noisy linear observation model with an unknown permutation, based on observing $y = \Pi^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $\Pi^*$ is an unknown $n \times n$ permutation matrix, and $w \in…
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however…
The three cardinal, statistically consistent, families of non-parametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…