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The paper proposes a specification test based on two estimates of distribution function. One is the traditional kernel distribution function estimate and the other is a newly proposed convolution-type distribution function estimate.…
We propose a family of weighted statistics based on the CUSUM process of the WLS residuals for the online detection of changepoints in a Random Coefficient Autoregressive model, using both the standard CUSUM and the Page-CUSUM process. We…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…
The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series,…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
For uniform random permutations conditioned to have no long cycles, we prove that the total number of cycles satisfies a central limit theorem. Under additional assumptions on the asymptotic behavior of the set of allowed cycle lengths, we…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
One of the most widely applied unit root test, Phillips-Perron test, enjoys in general highpowers, but suffers from size distortions when moving average noise exists. As a remedy, thispaper proposes a nonparametric bootstrap unit root test…
We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramer-von Mises type is proposed and its asymptotic behavior is studied. We show that under null…
The problem of quickest change detection in a sequence of independent observations is considered. The pre-change distribution is assumed to be known, while the post-change distribution is completely unknown. A window-limited leave-one-out…
We study the distribution of Durbin-Wu-Hausman (DWH) and Revankar-Hartley (RH) tests for exogeneity from a finite-sample viewpoint, under the null and alternative hypotheses. We consider linear structural models with possibly non-Gaussian…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy…
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…
In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…
Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and…