5,067 research outputs found
Comparison of Estimators in GLM with Binary Data
Maximum likelihood estimates (MLE) of regression parameters in the generalized linear models (GLM) are biased and their bias is non negligible when sample size is small. This study focuses on the GLM with binary data with multiple observations on response for each predictor value when sample size is small. The performance of the estimation methods in Cordeiro and McCullagh (1991), Firth (1993) and Pardo et al. (2005) are compared for GLM with binary data using an extensive Monte Carlo simulation study. Performance of these methods for three real data sets is also compared
On the Properties of Simulation-based Estimators in High Dimensions
Considering the increasing size of available data, the need for statistical
methods that control the finite sample bias is growing. This is mainly due to
the frequent settings where the number of variables is large and allowed to
increase with the sample size bringing standard inferential procedures to incur
significant loss in terms of performance. Moreover, the complexity of
statistical models is also increasing thereby entailing important computational
challenges in constructing new estimators or in implementing classical ones. A
trade-off between numerical complexity and statistical properties is often
accepted. However, numerically efficient estimators that are altogether
unbiased, consistent and asymptotically normal in high dimensional problems
would generally be ideal. In this paper, we set a general framework from which
such estimators can easily be derived for wide classes of models. This
framework is based on the concepts that underlie simulation-based estimation
methods such as indirect inference. The approach allows various extensions
compared to previous results as it is adapted to possibly inconsistent
estimators and is applicable to discrete models and/or models with a large
number of parameters. We consider an algorithm, namely the Iterative Bootstrap
(IB), to efficiently compute simulation-based estimators by showing its
convergence properties. Within this framework we also prove the properties of
simulation-based estimators, more specifically the unbiasedness, consistency
and asymptotic normality when the number of parameters is allowed to increase
with the sample size. Therefore, an important implication of the proposed
approach is that it allows to obtain unbiased estimators in finite samples.
Finally, we study this approach when applied to three common models, namely
logistic regression, negative binomial regression and lasso regression
Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations
Variational Bayes (VB) methods have emerged as a fast and
computationally-efficient alternative to Markov chain Monte Carlo (MCMC)
methods for scalable Bayesian estimation of mixed multinomial logit (MMNL)
models. It has been established that VB is substantially faster than MCMC at
practically no compromises in predictive accuracy. In this paper, we address
two critical gaps concerning the usage and understanding of VB for MMNL. First,
extant VB methods are limited to utility specifications involving only
individual-specific taste parameters. Second, the finite-sample properties of
VB estimators and the relative performance of VB, MCMC and maximum simulated
likelihood estimation (MSLE) are not known. To address the former, this study
extends several VB methods for MMNL to admit utility specifications including
both fixed and random utility parameters. To address the latter, we conduct an
extensive simulation-based evaluation to benchmark the extended VB methods
against MCMC and MSLE in terms of estimation times, parameter recovery and
predictive accuracy. The results suggest that all VB variants with the
exception of the ones relying on an alternative variational lower bound
constructed with the help of the modified Jensen's inequality perform as well
as MCMC and MSLE at prediction and parameter recovery. In particular, VB with
nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta)
is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an
attractive alternative to MCMC and MSLE for fast, scalable and accurate
estimation of MMNL models
Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines
DNA copy number and mRNA expression are widely used data types in cancer
studies, which combined provide more insight than separately. Whereas in
existing literature the form of the relationship between these two types of
markers is fixed a priori, in this paper we model their association. We employ
piecewise linear regression splines (PLRS), which combine good interpretation
with sufficient flexibility to identify any plausible type of relationship. The
specification of the model leads to estimation and model selection in a
constrained, nonstandard setting. We provide methodology for testing the effect
of DNA on mRNA and choosing the appropriate model. Furthermore, we present a
novel approach to obtain reliable confidence bands for constrained PLRS, which
incorporates model uncertainty. The procedures are applied to colorectal and
breast cancer data. Common assumptions are found to be potentially misleading
for biologically relevant genes. More flexible models may bring more insight in
the interaction between the two markers.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS605 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks
We present a procedure for effective estimation of entropy and mutual
information from small-sample data, and apply it to the problem of inferring
high-dimensional gene association networks. Specifically, we develop a
James-Stein-type shrinkage estimator, resulting in a procedure that is highly
efficient statistically as well as computationally. Despite its simplicity, we
show that it outperforms eight other entropy estimation procedures across a
diverse range of sampling scenarios and data-generating models, even in cases
of severe undersampling. We illustrate the approach by analyzing E. coli gene
expression data and computing an entropy-based gene-association network from
gene expression data. A computer program is available that implements the
proposed shrinkage estimator.Comment: 18 pages, 3 figures, 1 tabl
Marginal Likelihood Estimation with the Cross-Entropy Method
We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. This approach is motivated by the difficulty of obtaining an accurate estimate through existing algorithms that use Markov chain Monte Carlo (MCMC) draws, where the draws are typically costly to obtain and highly correlated in high-dimensional settings. In contrast, we use the cross-entropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rare-event simulation. The main advantage of the importance sampling approach is that random samples can be obtained from some convenient density with little additional costs. As we are generating independent draws instead of correlated MCMC draws, the increase in simulation effort is much smaller should one wish to reduce the numerical standard error of the estimator. Moreover, the importance density derived via the CE method is in a well-defined sense optimal. We demonstrate the utility of the proposed approach by two empirical applications involving women's labor market participation and U.S. macroeconomic time series. In both applications the proposed CE method compares favorably to existing estimators
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