Resampling

About: Resampling is a research topic. Over the lifetime, 5428 publications have been published within this topic receiving 242291 citations.

Negative association, ordering and convergence of resampling methods

Abstract: We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of measures output from Kitagawa's (1996) stratified resampling method. Carpenter et al's (1999) systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of Srinivasan (2001), which shares some attractive properties of systematic resampling, but which exhibits negative association and therefore converges irrespective of the order of the input samples. We confirm a conjecture made by Kitagawa (1996) that ordering input samples by their states in $\mathbb{R}$ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in $\mathbb{R}^d$, the variance of the resampling error is ${\scriptscriptstyle\mathcal{O}}(N^{-(1+1/d)})$ under mild conditions, where $N$ is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.

Subsampling Sequential Monte Carlo for Static Bayesian Models

Abstract: We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.

Inference on parameter sets in econometric models

Abstract: This paper provides confidence regions for minima of an econometric criterion function Q(θ). The minima form a set of parameters, ΘI , called the identified set. In economic applications, ΘI represents a class of economic models that are consistent with the data. Our inference procedures are criterion function based and so our confidence regions, which cover ΘI with a prespecified probability, are appropriate level sets of Qn(θ), the sample analog of Q(θ). When ΘI is a singleton, our confidence sets reduce to the conventional confidence regions based on inverting the likelihood or other criterion functions. We show that our procedure is valid under general yet simple conditions, and we provide feasible resampling procedure for implementing the approach in practice. We then show that these general conditions hold in a wide class of parametric econometric models. In order to verify the conditions, we develop methods of analyzing the asymptotic behavior of econometric criterion functions under set identification and also characterize the rates of convergence of the confidence regions to the identified set. We apply our methods to regressions with interval data and set identified method of moments problems. We illustrate our methods in an empirical Monte Carlo study based on Current Population Survey data.

Statistics and Data Analysis for Financial Engineering: with R examples

Abstract: Introduction.- Returns.- Fixed income securities.- Exploratory data analysis.- Modeling univariate distributions.- Resampling.- Multivariate statistical models.- Copulas.- Time series models: basics.- Time series models: further topics.- Portfolio theory.- Regression: basics.- Regression: troubleshooting.- Regression: advanced topics.- Cointegration.- The capital asset pricing model.- Factor models and principal components.- GARCH models.- Risk management.- Bayesian data analysis and MCMC.- Nonparametric regression and splines.