26,720 research outputs found
Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model
This paper develops a bias correction scheme for a multivariate
heteroskedastic errors-in-variables model. The applicability of this model is
justified in areas such as astrophysics, epidemiology and analytical chemistry,
where the variables are subject to measurement errors and the variances vary
with the observations. We conduct Monte Carlo simulations to investigate the
performance of the corrected estimators. The numerical results show that the
bias correction scheme yields nearly unbiased estimates. We also give an
application to a real data set.Comment: 12 pages. Statistical Paper
Derivative Computations and Robust Standard Errors for Linear Mixed Effects Models in lme4
While robust standard errors and related facilities are available in R for
many types of statistical models, the facilities are notably lacking for models
estimated via lme4. This is because the necessary statistical output, including
the Hessian and casewise gradient of random effect parameters, is not
immediately available from lme4 and is not trivial to obtain. In this article,
we supply and describe two new functions to obtain this output from Gaussian
mixed models: estfun.lmerMod() and vcov.full.lmerMod(). We discuss the
theoretical results implemented in the code, focusing on calculation of robust
standard errors via package sandwich. We also use the Sleepstudy data to
illustrate the code and compare it to a benchmark from package lavaan.Comment: Accepted at Journal of Statistical Softwar
Joint constraints on galaxy bias and through the N-pdf of the galaxy number density
We present a full description of the N-probability density function of the
galaxy number density fluctuations. This N-pdf is given in terms, on the one
hand, of the cold dark matter correlations and, on the other hand, of the
galaxy bias parameter. The method relies on the assumption commonly adopted
that the dark matter density fluctuations follow a local non-linear
transformation of the initial energy density perturbations. The N-pdf of the
galaxy number density fluctuations allows for an optimal estimation of the bias
parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if
there exists any a priori information on the bias parameter), and of those
parameters defining the dark matter correlations, in particular its amplitude
(). It also provides the proper framework to perform model selection
between two competitive hypotheses. The parameters estimation capabilities of
the N-pdf are proved by SDSS-like simulations (both ideal log-normal
simulations and mocks obtained from Las Damas simulations), showing that our
estimator is unbiased. We apply our formalism to the 7th release of the SDSS
main sample (for a volume-limited subset with absolute magnitudes ). We obtain and , for galaxy number density fluctuations in cells of a size of
Mpc. Different model selection criteria show that galaxy biasing is
clearly favoured.Comment: 25 pages, 9 figures, 2 tables. v2: Substantial revision, adding the
joint constraints with \sigma_8 and testing with Las Damas mocks. Matches
version accepted for publication in JCA
Fisher Lecture: Dimension Reduction in Regression
Beginning with a discussion of R. A. Fisher's early written remarks that
relate to dimension reduction, this article revisits principal components as a
reductive method in regression, develops several model-based extensions and
ends with descriptions of general approaches to model-based and model-free
dimension reduction in regression. It is argued that the role for principal
components and related methodology may be broader than previously seen and that
the common practice of conditioning on observed values of the predictors may
unnecessarily limit the choice of regression methodology.Comment: This paper commented in: [arXiv:0708.3776], [arXiv:0708.3777],
[arXiv:0708.3779]. Rejoinder in [arXiv:0708.3781]. Published at
http://dx.doi.org/10.1214/088342306000000682 in the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
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