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Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Following the line of classification-based two-sample testing, tests based on the Random Forest classifier are proposed. The developed tests are easy to use, require almost no tuning, and are applicable for any distribution on…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
We have developed an algorithm that numericaly computes the dimension of an extremely inhomogeous matter distribution, given by a discrete hierarchical metric. With our results it is possible to analise how the dimension of the matter…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
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…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…