Estimating the number of classes

DOI10.1214/009053606000001280zbMath1117.62045arXiv0708.2153OpenAlexW2136928476MaRDI QIDQ995434

Chang Xuan Mao, Bruce G. Lindsay

Publication date: 3 September 2007

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2153

zbMATH Keywords

moment problemHankel matrixone-sided inference

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Nonparametric tolerance and confidence regions (62G15)

Related Items (24)

A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments ⋮ Bayesian model averaging for estimating the number of classes: applications to the total number of species in metagenomics ⋮ Concentration inequality for evolutionary trees ⋮ Estimating population sizes with the Rasch model ⋮ Nonparametric estimation of species richness using discrete \(k\)-monotone distributions ⋮ Capture-recapture estimation based upon the geometric distribution allowing for heterogeneity ⋮ Petersen estimator, Chapman adjustment, list effects, and heterogeneity ⋮ Completely monotone distributions: mixing, approximation and estimation of number of species ⋮ Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments ⋮ Nonparametric species richness estimation under convexity constraint ⋮ A modified bootstrap procedure for cluster sampling variance estimation of species richness ⋮ On the Nonidentifiability of Population Sizes ⋮ LOWER BOUNDS TO THE POPULATION SIZE WHEN CAPTURE PROBABILITIES VARY OVER INDIVIDUALS ⋮ Chebyshev polynomials, moment matching, and optimal estimation of the unseen ⋮ On the Chao and Zelterman estimators in a binomial mixture model ⋮ A correction to make Chao estimator conservative when the number of sampling occasions is finite ⋮ Estimating diversity via frequency ratios ⋮ Thirty years of progeny from Chao’s inequality: Estimating and comparing richness with incidence data and incomplete sampling ⋮ Small-Sample Estimation of Species Richness Applied to Forest Communities ⋮ Sequential search algorithm for estimation of the number of members of a given population ⋮ Estimating Abundance from Presence–Absence Maps via a Paired Negative‐Binomial Model ⋮ Estimating population sizes for capture-recapture sampling with binomial mixtures ⋮ A modification of Chao's lower bound estimator in the case of one-inflation ⋮ On Population Size Estimators in the Poisson Mixture Model

Cites Work

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• Tests and diagnostics for heterogeneity in the species problem
• The geometry of mixture likelihoods: A general theory
• One-sided inference about functionals of a density
• Pseudo maximum likelihood estimation: Theory and applications
• The nonexistence of confidence sets for discontinuous functionals.
• Nonexistence of informative unbiased estimators in singular problems
• Estimating the Number of Species in a Stochastic Abundance Model
• The Nonexistence of Certain Statistical Procedures in Nonparametric Problems
• A Note on Capture-Recapture Estimation
• Estimating the Number of Classes via Sample Coverage
• A note on the upper bound for the distance in total variation between the binomal and the Poisson distribution
• Estimating the Complete Sample Size from an Incomplete Poisson Sample
• Predicting the Conditional Probability of Discovering a New Class
• Estimating the number of classes in multiple populations: A geometric analysis

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