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How best to estimate the accuracy of a predictive rule has been a longstanding question in statistics. Approaches to this task range from simple methods like Mallow’s Cp to algorithmic techniques l...

In this article I review the modeling of capture, recapture, and removal statistics for the purpose of estimating demographic parameters of fish and wildlife populations. Topics considered include capture-recapture models, band or tag return models, removal and catch per unit effort models, selective removal or change-in-ratio models, radio-tagging survival models, and nest survival models. The purpose is to present important concepts in a general manner for the benefit of a wide audience of statisticians. I will not attempt to be comprehensive, and I indulge in speculation about future directions. I indicate the importance of different statistical tools to this subject, such as Bayesian inference, “boot strapping,” robustness studies, goodness-of-fit tests. I also emphasize connections to other application areas of statistics. Capture-recapture methods, for example, are being considered for estimation of a variety of elusive human populations, such as the homeless and people missed in the census...

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject. The early density estimation methods, such as the histogram, kernel estimators, and orthogonal series estimators are still very popular, and recent research on them is described. Different types of restricted maximum likelihood density estimators, including order-restricted estimators, maximum penalized likelihood estimators, and sieve estimators, are discussed, where re...

The determination of plotting positions on probability graph paper so that the associated weighted least squares estimators of the scale parameter and the percentiles of a continuous distribution have certain properties is discussed. Necessary and sufficient conditions are given for an invariant optimal plot for percentile estimation. Also discussed is the derivation of ordered plotting positions.