19,712 research outputs found
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
Random sets and exact confidence regions
An important problem in statistics is the construction of confidence regions
for unknown parameters. In most cases, asymptotic distribution theory is used
to construct confidence regions, so any coverage probability claims only hold
approximately, for large samples. This paper describes a new approach, using
random sets, which allows users to construct exact confidence regions without
appeal to asymptotic theory. In particular, if the user-specified random set
satisfies a certain validity property, confidence regions obtained by
thresholding the induced data-dependent plausibility function are shown to have
the desired coverage probability.Comment: 14 pages, 2 figure
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