Related papers: General Type Token Distribution
The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator…
We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…
The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
The evolutionary dynamics of molecular populations are strongly dependent on the structure of genotype spaces. The map between genotype and phenotype determines how easily genotype spaces can be navigated and the accessibility of…
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
Given samples from a distribution, how many new elements should we expect to find if we continue sampling this distribution? This is an important and actively studied problem, with many applications ranging from unseen species estimation to…
We consider the problem of counting $k$-tuples of positive integers satisfying any arbitrary set of gcd conditions, where every integer is not larger than $x$. We first establish the conditions to guarantee the existence of such tuples, and…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
The number partitioning problem can be interpreted physically in terms of a thermally isolated non-interacting Bose gas trapped in a one-dimensional harmonic oscillator potential. We exploit this analogy to characterize, by means of a…