1,307 research outputs found
Continuous record Laplace-based inference about the break date in structural change models
Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method.A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise—lower mean absolute error (MAE) and lower root-mean squared error (RMSE)—than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.First author draf
Asymptotics of the discrete log-concave maximum likelihood estimator and related applications
The assumption of log-concavity is a flexible and appealing nonparametric
shape constraint in distribution modelling. In this work, we study the
log-concave maximum likelihood estimator (MLE) of a probability mass function
(pmf). We show that the MLE is strongly consistent and derive its pointwise
asymptotic theory under both the well- and misspecified setting. Our asymptotic
results are used to calculate confidence intervals for the true log-concave
pmf. Both the MLE and the associated confidence intervals may be easily
computed using the R package logcondiscr. We illustrate our theoretical results
using recent data from the H1N1 pandemic in Ontario, Canada.Comment: 21 pages, 7 Figure
Generalized bootstrap for estimating equations
We introduce a generalized bootstrap technique for estimators obtained by
solving estimating equations. Some special cases of this generalized bootstrap
are the classical bootstrap of Efron, the delete-d jackknife and variations of
the Bayesian bootstrap. The use of the proposed technique is discussed in some
examples. Distributional consistency of the method is established and an
asymptotic representation of the resampling variance estimator is obtained.Comment: Published at http://dx.doi.org/10.1214/009053604000000904 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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