37,495 research outputs found
Beyond first-order asymptotics for Cox regression
To go beyond standard first-order asymptotics for Cox regression, we develop
parametric bootstrap and second-order methods. In general, computation of
-values beyond first order requires more model specification than is
required for the likelihood function. It is problematic to specify a censoring
mechanism to be taken very seriously in detail, and it appears that
conditioning on censoring is not a viable alternative to that. We circumvent
this matter by employing a reference censoring model, matching the extent and
timing of observed censoring. Our primary proposal is a parametric bootstrap
method utilizing this reference censoring model to simulate inferential
repetitions of the experiment. It is shown that the most important part of
improvement on first-order methods - that pertaining to fitting nuisance
parameters - is insensitive to the assumed censoring model. This is supported
by numerical comparisons of our proposal to parametric bootstrap methods based
on usual random censoring models, which are far more unattractive to implement.
As an alternative to our primary proposal, we provide a second-order method
requiring less computing effort while providing more insight into the nature of
improvement on first-order methods. However, the parametric bootstrap method is
more transparent, and hence is our primary proposal. Indications are that
first-order partial likelihood methods are usually adequate in practice, so we
are not advocating routine use of the proposed methods. It is however useful to
see how best to check on first-order approximations, or improve on them, when
this is expressly desired.Comment: Published at http://dx.doi.org/10.3150/13-BEJ572 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration
Bayesian approaches for handling covariate measurement error are well
established, and yet arguably are still relatively little used by researchers.
For some this is likely due to unfamiliarity or disagreement with the Bayesian
inferential paradigm. For others a contributory factor is the inability of
standard statistical packages to perform such Bayesian analyses. In this paper
we first give an overview of the Bayesian approach to handling covariate
measurement error, and contrast it with regression calibration (RC), arguably
the most commonly adopted approach. We then argue why the Bayesian approach has
a number of statistical advantages compared to RC, and demonstrate that
implementing the Bayesian approach is usually quite feasible for the analyst.
Next we describe the closely related maximum likelihood and multiple imputation
approaches, and explain why we believe the Bayesian approach to generally be
preferable. We then empirically compare the frequentist properties of RC and
the Bayesian approach through simulation studies. The flexibility of the
Bayesian approach to handle both measurement error and missing data is then
illustrated through an analysis of data from the Third National Health and
Nutrition Examination Survey
GAMLSS for high-dimensional data – a flexible approach based on boosting
Generalized additive models for location, scale and shape (GAMLSS) are a popular semi-parametric modelling approach that, in contrast to conventional GAMs, regress not only the expected mean but every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSS are infeasible for high-dimensional data setups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high-dimensional GAMLSS that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The proposed algorithm was applied to data of the Munich Rental Guide, which is used by
landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net-rent predictions that resulted from the high-dimensional GAMLSS were found to be highly competitive while covariate-specific prediction intervals showed a major improvement over classical GAMs
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