相关论文: Lower k-record values from unit-Gompertz distribut…

Generalized linear (GL-) statistics are defined as functionals of an U-quantile process and unify different classes of statistics such as U-statistics and L-statistics. We derive a central limit theorem for GL-statistics of strongly mixing…

We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…

Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…

The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…

Given $n$ samples from a population of individuals belonging to different species, what is the number $U$ of hitherto unseen species that would be observed if $\lambda n$ new samples were collected? This is an important problem in many…

We study nonparametric regression with covariates $X$ and outcome $Y$ under random unbiased perturbations (RUPs) of the conditional distribution $Y|X$, where the marginal distribution of covariates, $P^X$, remains fixed but the conditional…

Supplement 1 to GUM (GUM-S1) recommends the use of maximum entropy principle (MaxEnt) in determining the probability distribution of a quantity having specified properties, e.g., specified central moments. When we only know the mean value…

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

With generalizing the Brody distribution to include the Poisson, GOE and GUE limits and with employing the maximum likelihood estimation technique, the spectral statistics of different sequences were considered in the nearest neighbor…

We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…

Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where…

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…

The development of prior distributions for Bayesian regression has traditionally been driven by the goal of achieving sensible model selection and parameter estimation. The formalization of properties that characterize good performance has…

A new method to simulate probability distributions in regions where the events are VERY unlikely (e.g. p ~ 10^{-40}) is presented. The basic idea is to represent the underlying probability space by the phase space of a physical system. The…

Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze…

An inner-product Hilbert space formulation is defined over a domain of all permutations with ties upon the extended real line. We demonstrate this work to resolve the common first and second order biases found in the pervasive Kendall and…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…