Related papers: Wavelet eigenvalue regression in high dimensions
This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time…
We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
This paper proposes a new robust smooth-threshold estimating equation to select important variables and automatically estimate parameters for high dimensional longitudinal data. A novel working correlation matrix is proposed to capture…
In applied multivariate statistics, estimating the number of latent dimensions or the number of clusters, $k$, is a fundamental and recurring problem. We study a sequence of statistics called "cross-validated eigenvalues." Under a large…
This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence…
Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In…
High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…
We apply the approximate dynamics derived from the Gaussian time-dependent variational principle to the Hamiltonian $ \hat H= {1/2}(\hat p_x ^2+ \hat p_y ^2)+ {1/2}\hat x^2\hat y^2$, which is strongly chaotic in the classical limit. We are…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…
The increased use of low-cost gyroscopes within inertial sensors for navigation purposes, among others, has brought to the development of a considerable amount of research in improving their measurement precision. Aside from developing…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…