Related papers: Unlinked monotone regression
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone…
We study the monotone single index model where a real response variable $Y $ is linked to a $d$-dimensional covariate $X$ through the relationship $E[Y | X] = \Psi_0(\alpha^T_0 X)$ almost surely. Both the ridge function, $\Psi_0$, and the…
Conventionally, regression discontinuity analysis contrasts a univariate regression's limits as its independent variable, $R$, approaches a cut-point, $c$, from either side. Alternative methods target the average treatment effect in a small…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
Motivated by the simultaneous association analysis with the presence of latent confounders, this paper studies the large-scale hypothesis testing problem for the high-dimensional confounded linear models with both non-asymptotic and…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still…
Consider a regression problem where there is no labeled data and the only observations are the predictions $f_i(x_j)$ of $m$ experts $f_{i}$ over many samples $x_j$. With no knowledge on the accuracy of the experts, is it still possible to…
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from…
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…
In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from…
We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…
We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
Covariate adjustment can improve precision in analyzing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis.…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…