3,095 research outputs found
The wild bootstrap for multilevel models
In this paper we study the performance of the most popular bootstrap schemes
for multilevel data. Also, we propose a modified version of the wild bootstrap
procedure for hierarchical data structures. The wild bootstrap does not require
homoscedasticity or assumptions on the distribution of the error processes.
Hence, it is a valuable tool for robust inference in a multilevel framework. We
assess the finite size performances of the schemes through a Monte Carlo study.
The results show that for big sample sizes it always pays off to adopt an
agnostic approach as the wild bootstrap outperforms other techniques
Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels
The global sensitivity analysis method, used to quantify the influence of
uncertain input variables on the response variability of a numerical model, is
applicable to deterministic computer code (for which the same set of input
variables gives always the same output value). This paper proposes a global
sensitivity analysis methodology for stochastic computer code (having a
variability induced by some uncontrollable variables). The framework of the
joint modeling of the mean and dispersion of heteroscedastic data is used. To
deal with the complexity of computer experiment outputs, non parametric joint
models (based on Generalized Additive Models and Gaussian processes) are
discussed. The relevance of these new models is analyzed in terms of the
obtained variance-based sensitivity indices with two case studies. Results show
that the joint modeling approach leads accurate sensitivity index estimations
even when clear heteroscedasticity is present
Kernel conditional quantile estimation via reduction revisited
Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.
Asymptotic inference in some heteroscedastic regression models with long memory design and errors
This paper discusses asymptotic distributions of various estimators of the
underlying parameters in some regression models with long memory (LM) Gaussian
design and nonparametric heteroscedastic LM moving average errors. In the
simple linear regression model, the first-order asymptotic distribution of the
least square estimator of the slope parameter is observed to be degenerate.
However, in the second order, this estimator is -consistent and
asymptotically normal for ; nonnormal otherwise, where and are
LM parameters of design and error processes, respectively. The
finite-dimensional asymptotic distributions of a class of kernel type
estimators of the conditional variance function in a more general
heteroscedastic regression model are found to be normal whenever ,
and non-normal otherwise. In addition, in this general model,
-consistency of the local Whittle estimator of based on pseudo
residuals and consistency of a cross validation type estimator of
are established. All of these findings are then used to propose a lack-of-fit
test of a parametric regression model, with an application to some currency
exchange rate data which exhibit LM.Comment: Published in at http://dx.doi.org/10.1214/009053607000000686 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes
We propose a voxel-wise general linear model with autoregressive noise and
heteroscedastic noise innovations (GLMH) for analyzing functional magnetic
resonance imaging (fMRI) data. The model is analyzed from a Bayesian
perspective and has the benefit of automatically down-weighting time points
close to motion spikes in a data-driven manner. We develop a highly efficient
Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable
selection among the regressors to model both the mean (i.e., the design matrix)
and variance. This makes it possible to include a broad range of explanatory
variables in both the mean and variance (e.g., time trends, activation stimuli,
head motion parameters and their temporal derivatives), and to compute the
posterior probability of inclusion from the MCMC output. Variable selection is
also applied to the lags in the autoregressive noise process, making it
possible to infer the lag order from the data simultaneously with all other
model parameters. We use both simulated data and real fMRI data from OpenfMRI
to illustrate the importance of proper modeling of heteroscedasticity in fMRI
data analysis. Our results show that the GLMH tends to detect more brain
activity, compared to its homoscedastic counterpart, by allowing the variance
to change over time depending on the degree of head motion
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