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Regression is one of the most commonly used statistical techniques. However, testing regression systems is a great challenge because of the absence of test oracle in general. In this paper, we show that Metamorphic Testing is an effective…
For a regression problem with a binary label response, we examine the problem of constructing confidence intervals for the label probability conditional on the features. In a setting where we do not have any information about the underlying…
We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
Quantile regression is used to study effects of covariates on a particular quantile of the data distribution. Here we are interested in the question whether a covariate has any effect on the entire data distribution, i.e., on any of the…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
The scope of this paper is the presentation of a test that enables to detect heteroscedasticity in univariate regression model. The test is simple to compute and very general since no hypothesis is made on the regularity of the response…
The standard method of transforming a continuous distribution on the line to the uniform distribution on the unit interval is the probability integral transform. Analogous transforms exist on compact Riemannian manifolds, in that, for each…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…