相关论文: Better lower bounds for missing species: improved …
The statistical problem of using an initial sample to estimate the number of species in a larger sample has found important applications in fields far removed from ecology. Here we address the general problem of estimating the number of…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
As one of the most commonly seen data challenges, missing data, in particular, multiple, non-monotone missing patterns, complicates estimation and inference due to the fact that missingness mechanisms are often not missing at random, and…
This paper proposes a simple and efficient estimation procedure for the model with non-ignorable missing data studied by Morikawa and Kim (2016). Their semiparametrically efficient estimator requires explicit nonparametric estimation and so…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we…
We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by…
In ecology, the description of species composition and biodiversity calls for statistical methods that involve estimating features of interest in unobserved samples based on an observed one. In the last decade, the Bayesian nonparametrics…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM…
In this work we study the {\it moment estimation} problem using weighted sampling. Given sample access to a set $A$ with $n$ weighted elements, and a parameter $t>0$, we estimate the $t$-th moment of $A$ given as $S_t=\sum_{a\in A} w(a)^t$.…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin…
In ecological studies niche overlap is often used to quantify species interaction and dynamics. This paper develops a robust, nonparametric statistical framework for quantifying and analyzing multivariate niche overlap. Parametric methods…
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…