Related papers: Choice of the hypothesis matrix for using the Wald…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
Let $\Sigma_d^{++}$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying any two $SL_d(\mathbb{Z})$-congruent elements in $\Sigma_d^{++}$ gives rise to the space of reduced quadratic forms of…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
Estimation of the proportion of null hypotheses in a multiple testing problem can greatly enhance the performance of the existing algorithms. Although various estimators for the proportion of null hypotheses have been proposed, most are…
We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are…
When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is…
Statistical analysis is often used to evaluate the evidence for or against scientific hypotheses, and various statistics (e.g., p-values, likelihood ratios, Bayes factors) are interpreted as measures of evidence strength. Here I consider…
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…
This paper develops a hybrid likelihood (HL) method based on a compromise between parametric and nonparametric likelihoods. Consider the setting of a parametric model for the distribution of an observation $Y$ with parameter $\theta$.…
Consider the following parameterized counting variation of the classic subset sum problem, which arises notably in the context of higher homotopy groups of topological spaces: Let $\mathbf{v} \in \mathbb{Q}^d$ be a rational vector, $(T_{1},…
Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
A standard practice in statistical hypothesis testing is to mention the p-value alongside the accept/reject decision. We show the advantages of mentioning an e-value instead. With p-values, it is not clear how to use an extreme observation…
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…