Estimating Marginal Hazard Ratios by Simultaneously Using A Set of Propensity Score Models: A Multiply Robust Approach

The inverse probability weighted Cox model is frequently used to estimate marginal hazard ratios. Its validity requires a crucial condition that the propensity score model is correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux-en-Y gastric bypass using data from a large medical claims and billing database.We further extend the development to multi-site studies to enable each site to postulate multiple site-specific propensity score models

Rejoinder: Matched Pairs and the Future of Cluster-Randomized Experiments

Rejoinder to "The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insurance Evaluation" [arXiv:0910.3752]Comment: Published in at http://dx.doi.org/10.1214/09-STS274REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods

Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to extract this information from the observations. We derive minimum variance estimators for projected density reconstruction and its power spectrum and apply them to simulated data sets, showing that they give a good agreement with the theoretical minimum variance expectations. The same estimator can also be applied to the cluster reconstruction, where it remains a useful reconstruction technique, although it is no longer optimal for every application. The method can be generalized to include nonlinear cluster reconstruction and photometric information on redshifts of background galaxies in the analysis. We also address the question of how to obtain directly the 3-d power spectrum from the weak lensing data. We derive a minimum variance quadratic estimator, which maximizes the likelihood function for the 3-d power spectrum and can be computed either from the measurements directly or from the 2-d power spectrum. The estimator correctly propagates the errors and provides a full correlation matrix of the estimates. It can be generalized to the case where redshift distribution depends on the galaxy photometric properties, which allows one to measure both the 3-d power spectrum and its time evolution.Comment: revised version, 36 pages, AAS LateX, submitted to Ap

Exit polling and racial bloc voting: Combining individual-level and R×\timesC ecological data

Despite its shortcomings, cross-level or ecological inference remains a necessary part of some areas of quantitative inference, including in United States voting rights litigation. Ecological inference suffers from a lack of identification that, most agree, is best addressed by incorporating individual-level data into the model. In this paper we test the limits of such an incorporation by attempting it in the context of drawing inferences about racial voting patterns using a combination of an exit poll and precinct-level ecological data; accurate information about racial voting patterns is needed to assess triggers in voting rights laws that can determine the composition of United States legislative bodies. Specifically, we extend and study a hybrid model that addresses two-way tables of arbitrary dimension. We apply the hybrid model to an exit poll we administered in the City of Boston in 2008. Using the resulting data as well as simulation, we compare the performance of a pure ecological estimator, pure survey estimators using various sampling schemes and our hybrid. We conclude that the hybrid estimator offers substantial benefits by enabling substantive inferences about voting patterns not practicably available without its use.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS353 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Partially Reflecting Random Walk on Spheres Algorithm for Electrical Impedance Tomography

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance of the new estimator both theoretically and experimentally. In a second step, the variance is considerably reduced via a novel control variate conditional sampling technique

Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods

This paper addresses the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated to polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. This paper shows that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three or four images. The proposed estimators provide better performance that the estimators of moments. These results are illustrated by estimations conducted on synthetic and real images

Finite Dimensional Statistical Inference

In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions, as well as correlated zero mean Wishart distributions. The tools used extend those of the free probability framework, which have been quite successful for high dimensional statistical inference (when the size of the matrices tends to infinity), also known as free deconvolution. This contribution focuses on the finite Gaussian case and proposes algorithmic methods to compute the moments. Cases where asymptotic results fail to apply are also discussed.Comment: 14 pages, 13 figures. Submitted to IEEE Transactions on Information Theor