Related papers: Wavelet eigenvalue regression in high dimensions
In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…
Variational Autoencoders (VAEs) are powerful generative models capable of learning compact latent representations. However, conventional VAEs often generate relatively blurry images due to their assumption of an isotropic Gaussian latent…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…