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Biometrika Advance Access





Published: Sat, 20 Jan 2018 00:00:00 GMT

Last Build Date: Sat, 20 Jan 2018 05:47:42 GMT

 



On the asymptotic efficiency of approximate Bayesian computation estimators

Sat, 20 Jan 2018 00:00:00 GMT

Summary
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large data limit. Our key assumption is that the data are summarized by a fixed-dimensional summary statistic that obeys a central limit theorem. We prove asymptotic normality of the mean of the approximate Bayesian computation posterior. This result also shows that, in terms of asymptotic variance, we should use a summary statistic that is of the same dimension as the parameter vector, $p$, and that any summary statistic of higher dimension can be reduced, through a linear transformation, to dimension $p$ in a way that can only reduce the asymptotic variance of the posterior mean. We look at how the Monte Carlo error of an importance sampling algorithm that samples from the approximate Bayesian computation posterior affects the accuracy of estimators. We give conditions on the importance sampling proposal distribution such that the variance of the estimator will be of the same order as that of the maximum likelihood estimator based on the summary statistics used. This suggests an iterative importance sampling algorithm, which we evaluate empirically on a stochastic volatility model.



Testing independence for multivariate time series via the auto-distance correlation matrix

Sat, 20 Jan 2018 00:00:00 GMT

Summary
We introduce the matrix multivariate auto-distance covariance and correlation functions for time series, discuss their interpretation and develop consistent estimators for practical implementation. We also develop a test of the independent and identically distributed hypothesis for multivariate time series data and show that it performs better than the multivariate Ljung–Box test. We discuss computational aspects and present a data example to illustrate the method.



Dual regression

Fri, 19 Jan 2018 00:00:00 GMT

Summary
We propose dual regression as an alternative to quantile regression for the global estimation of conditional distribution functions. Dual regression provides the interpretational power of quantile regression while avoiding the need to repair intersecting conditional quantile surfaces. We introduce a mathematical programming characterization of conditional distribution functions which, in its simplest form, is the dual program of a simultaneous estimator for linear location-scale models, and use it to specify and estimate a flexible class of conditional distribution functions. We present asymptotic theory for the corresponding empirical dual regression process.



Scalar-on-image regression via the soft-thresholded Gaussian process

Fri, 19 Jan 2018 00:00:00 GMT

Summary
This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational algorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian process prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size. The proposed method is compared to alternatives via simulation and applied to an electroencephalography study of alcoholism.