Related papers: A Linear-Time Kernel Goodness-of-Fit Test
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…
Consider an observation of a multivariate temporal point process $N$ with law $\mathcal P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathcal P$ belongs to a given parametric family, we construct a convergent…
It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated --…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…
In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…
\textbf{Purpose:} Amplitude analysis is a pivotal tool in hadron spectroscopy, fundamentally involving a series of likelihood fits to multi-dimensional experimental distributions. While robust goodness-of-fit tests exist for low-dimensional…
We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This…
After an elementary derivation of the "time transformation", mapping a counting process onto a homogeneous Poisson process with rate one, a brief review of Ogata's goodness of fit tests is presented and a new test, the "Wiener process…
This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual…
New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that…
We consider a regression model with errors that are a.s. negative. Thus the regression function is not the expected value of the observations but the right endpoint of their support. We develop two goodness-of-fit tests for the hypotheses…
We consider adaptive group testing in the linear regime, where the number of defective items scales linearly with the number of items. We analyse an algorithm based on generalized binary splitting. Provided fewer than half the items are…
We present the first method for assessing the relevance of a model-based clustering result in a general framework. Standard validation criteria, like the adjusted Rand index, rely on external labels to assess partition accuracy;…
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
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…
Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing…
A sizable amount of goodness-of-fit tests involving functional data have appeared in the last decade. We provide a relatively compact revision of most of these contributions, within the independent and identically distributed framework, by…