17,028 research outputs found
mistr: A Computational Framework for Mixture and Composite Distributions
Finite mixtures and composite distributions allow to model the probabilistic representation of data with more generality than simple distributions and are useful to consider in a wide range of applications. The R package mistr provides an extensible computational framework for creating, transforming, and evaluating these models, together with multiple methods for their visualization and description. In this paper we present the main computational framework of the package and illustrate its application. In addition, we provide and show functions for data modeling using two specific composite distributions as well as a numerical example where a composite distribution is estimated to describe the log-returns of selected stocks
Generalized Quantile Treatment Effect: A Flexible Bayesian Approach Using Quantile Ratio Smoothing
We propose a new general approach for estimating the effect of a binary
treatment on a continuous and potentially highly skewed response variable, the
generalized quantile treatment effect (GQTE). The GQTE is defined as the
difference between a function of the quantiles under the two treatment
conditions. As such, it represents a generalization over the standard
approaches typically used for estimating a treatment effect (i.e., the average
treatment effect and the quantile treatment effect) because it allows the
comparison of any arbitrary characteristic of the outcome's distribution under
the two treatments. Following Dominici et al. (2005), we assume that a
pre-specified transformation of the two quantiles is modeled as a smooth
function of the percentiles. This assumption allows us to link the two quantile
functions and thus to borrow information from one distribution to the other.
The main theoretical contribution we provide is the analytical derivation of a
closed form expression for the likelihood of the model. Exploiting this result
we propose a novel Bayesian inferential methodology for the GQTE. We show some
finite sample properties of our approach through a simulation study which
confirms that in some cases it performs better than other nonparametric
methods. As an illustration we finally apply our methodology to the 1987
National Medicare Expenditure Survey data to estimate the difference in the
single hospitalization medical cost distributions between cases (i.e., subjects
affected by smoking attributable diseases) and controls.Comment: Published at http://dx.doi.org/10.1214/14-BA922 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Model misspecification in peaks over threshold analysis
Classical peaks over threshold analysis is widely used for statistical
modeling of sample extremes, and can be supplemented by a model for the sizes
of clusters of exceedances. Under mild conditions a compound Poisson process
model allows the estimation of the marginal distribution of threshold
exceedances and of the mean cluster size, but requires the choice of a
threshold and of a run parameter, , that determines how exceedances are
declustered. We extend a class of estimators of the reciprocal mean cluster
size, known as the extremal index, establish consistency and asymptotic
normality, and use the compound Poisson process to derive misspecification
tests of model validity and of the choice of run parameter and threshold.
Simulated examples and real data on temperatures and rainfall illustrate the
ideas, both for estimating the extremal index in nonstandard situations and for
assessing the validity of extremal models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS292 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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