Related papers: Wavelet eigenvalue regression in high dimensions

The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

This paper considers estimating a covariance matrix of $p$ variables from $n$ observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these…

We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…

We apply variational-wavelet approach for constructing multiscale high-localized eigenmodes expansions in different models of nonlinear waves. We demonstrate appearance of coherent localized structures and stable pattern formation in…

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…

In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…

In this paper, we propose a novel method for estimating the long-memory parameter in time series. By combining the multi-resolution framework of wavelets with the robustness of the Least Absolute Deviations (LAD) criterion, we introduce a…

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…

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…

Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time…

We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…

This paper proposes a nonparametric Bayesian framework called VariScan for simultaneous clustering, variable selection, and prediction in high-throughput regression settings. Poisson-Dirichlet processes are utilized to detect…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

In the multidimensional setting, we consider the errors-in-variables model. We aim at estimating the unknown nonparametric multivariate regression function with errors in the covariates. We devise an adaptive estimator based on projection…

In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…

In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity.

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…