Related papers: Testing Functional Inequalities
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
Conformal inference is a versatile tool for building prediction sets in regression or classification. We study the false coverage proportion (FCP) in a simultaneous inference setting with a calibration sample of $n$ points and a test sample…
In this article, we propose a new class of consistent tests for $p$-variate normality. These tests are based on the characterization of the standard multivariate normal distribution, that the Hessian of the corresponding cumulant generating…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
This paper studies the problem of nonparametric testing for the effect of a random functional covariate on a real-valued error term. The covariate takes values in $L^2[0,1]$, the Hilbert space of the square-integrable real-valued functions…
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…
Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…
There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this…
We consider a stationary $AR(p)$ model. The autoregression parameters are unknown as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of empirical distribution function is defined and…
We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust…
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically,…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
With direct and simple proofs, we establish Poincar\'{e} type inequalities (including Poincar\'{e} inequalities, weak Poincar\'{e} inequalities and super Poincar\'{e} inequalities), entropy inequalities and Beckner-type inequalities for…