Asymptotic consistency under large entropy sampling designs with unequal probabilities

A large part of survey sampling literature is devoted to unequal probabilities sampling designs without replacement. Brewer and Hanif (1983) provided a summary of these sampling designs. The maximum entropy designs is one of them. Consistency results have been proven for the maximum entropy sampling (Hájek, 1964). The aim is to give sufficient conditions under which Hájek (1964) consistency results still hold for large entropy sampling designs which are different from the maximum entropy design. These conditions involve modes of convergence of sampling designs towards the maximum entropy design. We show that these conditions are satisfied for the popular Rao-Sampford (Rao, 1965, Sampford, 1967) design. Our consistency results are applied to the Hájek (1964) simple variance estimator. This estimator does not require joint-inclusion probabilities and can be easily estimated using weighted least squares regression (Berger, 2004, 2005b). Deville (1999) conjectured that this estimator is suitable for any sampling designs (see also Brewer and Donadio, 2003). Our consistency result gives regularity conditions under which this estimator is consistent which justifies Deville’s (1999) conjecture

Variance estimation for measures of change in probability sampling

We propose to estimate the design variance of absolute changes between two cross-sectional estimators under rotating sampling schemes. We show that the variance estimator proposed is generally positive. We also propose possible extensions for stratified samples, with dynamic stratification; that is, when units move between strata and new strata are created at the second waves

A simple variance estimator for unequal probability sampling without replacement

Survey sampling textbooks often refer to the Sen-Yates-Grundy variance estimator for use with without replacement unequal probability designs. This estimator is rarely implemented, because of the complexity of determining joint inclusion probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen-Hurwitz with replacement variance estimator; which often leads to overestimation of the variance for large sampling fraction that are common in business surveys. We will consider an alternative estimator: the Hájek (1964) variance estimator that depends on the first-order inclusion probabilities only and is usually more accurate than the Hansen-Hurwitz estimator. We review this estimator and show its practical value. We propose a simple alternative expression; which is as simple as the Hansen-Hurwitz estimator. We also show how the Hájek estimator can be easily implemented with standard statistical packages

Sparse image reconstruction on the sphere: analysis and synthesis

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l1 norm appearing in the regularisation problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353 GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.Comment: 11 pages, 6 Figure

Anisotropic flow in event-by-event ideal hydrodynamic simulations of sqrt(s_{NN})=200 GeV Au+Au collisions

We calculate flow observables with the NeXSPheRIO ideal hydrodynamic model and make the first comparison to the complete set of mid-rapidity flow measurements made by the PHENIX collaboration in top energy Au+Au collisions. A simultaneous calculation of v_2, v_3, v_4, and the first event-by-event calculation of quadrangular flow defined with respect to the v_2 event plane (v_4{Psi_2}) gives good agreement with measured values, including the dependence on both transverse momentum and centrality. This provides confirmation that the collision system is indeed well described as a quark-gluon plasma with an extremely small viscosity, and that correlations are dominantly generated from collective effects. In addition we present a prediction for v_5.Comment: 5 pages, 2 figures. Revised version. Corrections in eq.(7) and Fig.