180 research outputs found
Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
This paper considers the nonparametric maximum likelihood estimator (MLE) for
the joint distribution function of an interval censored survival time and a
continuous mark variable. We provide a new explicit formula for the MLE in this
problem. We use this formula and the mark specific cumulative hazard function
of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This
result leads to necessary and sufficient conditions for consistency of the MLE
which imply that the MLE is inconsistent in general. We show that the
inconsistency can be repaired by discretizing the marks. Our theoretical
results are supported by simulations.Comment: 27 pages, 4 figure
Strong Approximation of Empirical Copula Processes by Gaussian Processes
We provide the strong approximation of empirical copula processes by a
Gaussian process. In addition we establish a strong approximation of the
smoothed empirical copula processes and a law of iterated logarithm
Probing Loop Quantum Gravity with Evaporating Black Holes
This letter aims at showing that the observation of evaporating black holes
should allow distinguishing between the usual Hawking behavior and Loop Quantum
Gravity (LQG) expectations. We present a full Monte-Carlo simulation of the
evaporation in LQG and statistical tests that discriminate between competing
models. We conclude that contrarily to what was commonly thought, the
discreteness of the area in LQG leads to characteristic features that qualify
evaporating black holes as objects that could reveal quantum gravity
footprints.Comment: 5 pages, 3 figures. Version accpeted by Phys. Rev. Let
Random walks - a sequential approach
In this paper sequential monitoring schemes to detect nonparametric drifts
are studied for the random walk case. The procedure is based on a kernel
smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson
estimator and its as- sociated sequential partial sum process under
non-standard sampling. The asymptotic behavior differs substantially from the
stationary situation, if there is a unit root (random walk component). To
obtain meaningful asymptotic results we consider local nonpara- metric
alternatives for the drift component. It turns out that the rate of convergence
at which the drift vanishes determines whether the asymptotic properties of the
monitoring procedure are determined by a deterministic or random function.
Further, we provide a theoretical result about the optimal kernel for a given
alternative
Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting
The coefficient of determination, known as R2, is commonly used as a goodness-of-fit
criterion for fitting linear models. R2 is somewhat controversial when fitting nonlinear
models, although it may be generalised on a case-by-case basis to deal with specific models
such as the logistic model. Assume we are fitting a parametric distribution to a data set
using, say, the maximum likelihood estimation method. A general approach to measure
the goodness-of-fit of the fitted parameters, which is advocated herein, is to use a non-
parametric measure for comparison between the empirical distribution, comprising the
raw data, and the fitted model. In particular, for this purpose we put forward the Survi-
val Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) as a metric
which is bounded, and is a natural generalisation of the Jensen-Shannon divergence. We
demonstrate, via a straightforward procedure making use of the ESJS, that it can be used
as part of maximum likelihood estimation or curve fitting as a measure of goodness-of-fit,
including the construction of a confidence interval for the fitted parametric distribution.
Furthermore, we show the validity of the proposed method with simulated data, and three
empirical data sets
Bayesian methods and optimal experimental design for gene mapping by radiation hybrids
Radiation hybrid mapping is a somatic cell technique for ordering human loci along a chromosome and estimating the physical distance between adjacent loci. The present paper considers a realistic model of fragment generation and retention. This model assumes that fragments are generated in the ancestral cell of a clone according to a Poisson breakage process along the chromosome. Once generated, fragments are independently retained in the clone with a common retention probability. Based on this and less restrictive models, statistical criteria such as minimum obligate breaks, maximum likelihood, and Bayesian posterior probabilities can be used to decide order. Distances can be estimated by either maximum likelihood or Bayesian posterior means. The model also permits rational design of radiation dose for optimal statistical precision. A brief examination of some real data illustrates our criteria and computational algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65749/1/j.1469-1809.1992.tb01139.x.pd
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