相关论文: Composite Goodness-of-fit Tests with Kernels

Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

It has recently been shown that an unbinned distance-based statistic, the energy, can be used to construct an extremely powerful nonparametric multivariate two sample goodness-of-fit test. An extension to this method that makes it possible…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

This paper presents and examines computationally convenient goodness-of-fit tests for the family of generalized Poisson distributions, which encompasses notable distributions such as the Compound Poisson and the Katz distributions. The…

We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting…

The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…

We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…

Kernel-based testing has revolutionized the field of non-parametric tests through the embedding of distributions in an RKHS. This strategy has proven to be powerful and flexible, yet its applicability has been limited to the standard…