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Novel significance tests are proposed for the quite general additive concurrent model formulation without the need of model, error structure preliminary estimation or the use of tuning parameters. Making use of the martingale difference…
The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…
Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…
We propose a new method to test conditional independence of two real random variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$. %with $F_{.|.}$ representing conditional distribution functions, The partial copula…
Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…
In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance,…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
Scientists and practitioners increasingly rely on machine learning to model data and draw conclusions. Compared to statistical modeling approaches, machine learning makes fewer explicit assumptions about data structures, such as linearity.…