145,452 research outputs found
Approximate Profile Maximum Likelihood
We propose an efficient algorithm for approximate computation of the profile
maximum likelihood (PML), a variant of maximum likelihood maximizing the
probability of observing a sufficient statistic rather than the empirical
sample. The PML has appealing theoretical properties, but is difficult to
compute exactly. Inspired by observations gleaned from exactly solvable cases,
we look for an approximate PML solution, which, intuitively, clumps comparably
frequent symbols into one symbol. This amounts to lower-bounding a certain
matrix permanent by summing over a subgroup of the symmetric group rather than
the whole group during the computation. We extensively experiment with the
approximate solution, and find the empirical performance of our approach is
competitive and sometimes significantly better than state-of-the-art
performance for various estimation problems
Power delay profile and noise variance estimation for OFDM
In this letter, we present cyclic-prefix (CP) based noise-variance and power-delay-profile estimators for Orthogonal Frequency Division Multiplexing (OFDM) systems. Signal correlation due to the use of the CP is exploited without requiring additional pilot symbols. A heuristic estimator and a class of approximate maximum likelihood (ML) estimators are proposed. The proposed algorithms can be applied to both unitary and non-unitary constellations. These algorithms can be readily used for applications such as minimum mean-square error (MMSE) channel estimation
Modified Profile Likelihood Estimation in the Lomax Distribution
In this paper, we consider improving maximum likelihood inference for the scale parameter of the Lomax distribution. The improvement is based on using modifications to the maximum likelihood estimator based on the Barndorff-Nielsen modification of the profile likelihood function. We apply these modifications to obtain improved estimators for the scale parameter of the Lomax distribution in the presence of a nuisance shape parameter. Due to the complicated expression for the Barndorff-Nielsen’s modification, several approximations to this modification are considered in this paper, including the modification based on the empirical covariances and the approximation based on using suitably derived approximate ancillary statistics. We obtained the approximations for the Lomax profile likelihood function and the corresponding modified maximum likelihood estimators. They are not available in simple closed forms and can be obtained numerically as roots of some complicated likelihood equations. Comparisons between maximum profile likelihood estimator and modified profile likelihood estimators in terms of their biases and mean squared errors were carried out using simulation techniques. We found that the approximation based on the empirical covariances to have the best performance according to the criteria used. Therefore we recommend to use this modified version of the maximum likelihood estimator for the Lomax scale parameter, especially for small sample sizes with heavy censoring, which is quite common in industrial life testing experiments and reliability studies. An example based on real data is given to illustrate the methods considered in this paper.This research was supported by a grant from the Office of Research Support at Qatar University, grant no. QUST-2-CAS-2021-154
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Profile-score adjustments for incidental-parameter problems
We propose a scheme of iterative adjustments to the profile score to deal with incidental-parameter bias in models for stratified data with few observations on a large number of strata. The first-order adjustment is based on a calculation of the profile-score bias and evaluation of this bias at maximum-likelihood estimates of the incidental parameters. If the bias does not depend on the incidental parameters, the first-order adjusted profile score is fully recentered, solving the incidental-parameter problem. Otherwise, it is approximately recentered, alleviating the incidental-parameter problem. In the latter case, the adjustment can be iterated to give higher-order adjustments, possibly until convergence. The adjustments are generally applicable (e.g., not requiring parameter orthogonality) and lead to estimates that generally improve on maximum likelihood. We examine a range of nonlinear models with covariates. In many of them, we obtain an adjusted profile score that is exactly unbiased. In the others, we obtain approximate bias adjustments that yield much improved estimates, relative to maximum likelihood, even when there are only two observations per stratum
POOR PERFORMANCE OF BOOTSTRAP CONFIDENCE INTERVALS FOR THE LOCATION OF A QUANTITATIVE TRAIT LOUCS
The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTLs) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTLs are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the non-parametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals are poorly behaved and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately
Restricted maximum likelihood estimation in generalized linear mixed models
Restricted maximum likelihood (REML) estimation is a widely accepted and
frequently used method for fitting linear mixed models, with its principal
advantage being that it produces less biased estimates of the variance
components. However, the concept of REML does not immediately generalize to the
setting of non-normally distributed responses, and it is not always clear the
extent to which, either asymptotically or in finite samples, such
generalizations reduce the bias of variance component estimates compared to
standard unrestricted maximum likelihood estimation. In this article, we review
various attempts that have been made over the past four decades to extend REML
estimation in generalized linear mixed models. We establish four major classes
of approaches, namely approximate linearization, integrated likelihood,
modified profile likelihoods, and direct bias correction of the score function,
and show that while these four classes may have differing motivations and
derivations, they often arrive at a similar if not the same REML estimate. We
compare the finite sample performance of these four classes through a numerical
study involving binary and count data, with results demonstrating that they
perform similarly well in reducing the finite sample bias of variance
components
Approximate Integrated Likelihood via ABC methods
We propose a novel use of a recent new computational tool for Bayesian
inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC
is a way to handle models for which the likelihood function may be intractable
or even unavailable and/or too costly to evaluate; in particular, we consider
the problem of eliminating the nuisance parameters from a complex statistical
model in order to produce a likelihood function depending on the quantity of
interest only. Given a proper prior for the entire vector parameter, we propose
to approximate the integrated likelihood by the ratio of kernel estimators of
the marginal posterior and prior for the quantity of interest. We present
several examples.Comment: 28 pages, 8 figure
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