Related papers: Global testing under sparse alternatives: ANOVA, m…
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
We consider the problem where we have a multi-way table of means, indexed by several factors, where each factor can have a large number of levels. The entry in each cell is the mean of some response, averaged over the observations falling…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such…
In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…
We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…
Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function,…
For the single index model $y=f(\beta^{\tau}x,\epsilon)$ with Gaussian design, %satisfying that rank $var(\mathbb{E}[x\mid y])=1$ where $f$ is unknown and $\beta$ is a sparse $p$-dimensional unit vector with at most $s$ nonzero entries, we…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
This paper proposes a new procedure to validate the multi-factor pricing theory by testing the presence of alpha in linear factor pricing models with a large number of assets. Because the market's inefficient pricing is likely to occur to a…
Traditional analysis of variance (ANOVA) software allows researchers to test for the significance of main effects in the presence of interactions without exposure to the details of how the software encodes main effects and interactions to…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
We propose two algorithms for boosting random Fourier feature models for approximating high-dimensional functions. These methods utilize the classical and generalized analysis of variance (ANOVA) decomposition to learn low-order functions,…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
Analysis of covariance is a crucial method for improving precision of statistical tests for factor effects in randomized experiments. However, existing solutions suffer from one or more of the following limitations: (i) they are not…