Related papers: A New ECDF Two-Sample Test Statistic
A common disadvantage in existing distribution-free two-sample testing approaches is that the computational complexity could be high. Specifically, if the sample size is $N$, the computational complexity of those two-sample tests is at…
This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line…
The energy test method is a multi-dimensional test of whether two samples are consistent with arising from the same underlying population, through the calculation of a single test statistic (called the $T$-value). The method has recently…
In the context of the widely used competing risks set-up we discuss different inference procedures for testing equality of two cumulative incidence functions, where the data may be subject to independent right-censoring or left-truncation.…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
Empirical phi-divergence test-statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behaviour of the classical likelihood ratio test-statistic, as well asfor model misspecification…
The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov--Smirnov test based on the…
We construct a procedure to test the stochastic order of two samples of interval-valued data. We propose a test statistic which belongs to U-statistic and derive its asymptotic distribution under the null hypothesis. We compare the…
Based on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric $\alpha$-stable discrete parameter random field. We show that the power function converges to one as the sample-size…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
We discuss several tests for whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly…
Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…
Based on cumulative distribution functions, Fourier series expansion and Kolmogorov tests, we present a simple method to display probability densities for data drawn from a continuous distribution. It is often more efficient than using…
Hypothesis testing is a central problem in statistical analysis, and there is currently a lack of differentially private tests which are both statistically valid and powerful. In this paper, we develop several new differentially private…