Related papers: A test for normality based on self-similarity
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
Time Series Anomaly Detection (TSAD) finds widespread applications across various domains such as financial markets, industrial production, and healthcare. Its primary objective is to learn the normal patterns of time series data, thereby…
Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various proposed methods for solving this problem, classification-based methods, including one-class Support…
We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…
This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression…
The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…
The gold standard for identifying causal relationships is a randomized controlled experiment. In many applications in the social sciences and medicine, the researcher does not control the assignment mechanism and instead may rely upon…
Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for…
We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…
We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
In this article, we propose a one-sample test to check whether the support of the unknown distribution generating the data is homologically equivalent to the support of some specified distribution or not OR using the corresponding…