Efficient estimation of Banach parameters in semiparametric models

Consider a semiparametric model with a Euclidean parameter and an infinite-dimensional parameter, to be called a Banach parameter. Assume: (a) There exists an efficient estimator of the Euclidean parameter. (b) When the value of the Euclidean parameter is known, there exists an estimator of the Banach parameter, which depends on this value and is efficient within this restricted model. Substituting the efficient estimator of the Euclidean parameter for the value of this parameter in the estimator of the Banach parameter, one obtains an efficient estimator of the Banach parameter for the full semiparametric model with the Euclidean parameter unknown. This hereditary property of efficiency completes estimation in semiparametric models in which the Euclidean parameter has been estimated efficiently. Typically, estimation of both the Euclidean and the Banach parameter is necessary in order to describe the random phenomenon under study to a sufficient extent. Since efficient estimators are asymptotically linear, the above substitution method is a particular case of substituting asymptotically linear estimators of a Euclidean parameter into estimators that are asymptotically linear themselves and that depend on this Euclidean parameter. This more general substitution case is studied for its own sake as well, and a hereditary property for asymptotic linearity is proved.Comment: Published at http://dx.doi.org/10.1214/009053604000000913 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Calibrating Dark Energy

Exploring the diversity of dark energy dynamics, we discover a calibration relation, a uniform stretching of the amplitude of the equation of state time variation with scale factor. This defines homogeneous families of dark energy physics. The calibration factor has a close relation to the standard time variation parameter w_a, and we show that the new, calibrated w_a describes observables, i.e. distance and Hubble parameter as a function of redshift, typically to an accuracy level of 10^{-3}. We discuss implications for figures of merit for dark energy science programs.Comment: 9 pages, 10 figure

Special Issue about Competing Risks and Multi-State Models

There is a clear growing interest, at least in the statistical literature, in competing risks and multi-state models. With the rising interest in competing risks and multi-state models a number of software packages have been developed for the analysis of such models. The present special issue of the Journal of Statistical Software introduces a selection of R packages devoted to competing risks and multi-state models. This introduction to the special issue contains some background and highlights the contents of the contributions.

CMB Lensing Constraints on Neutrinos and Dark Energy

Signatures of lensing of the cosmic microwave background radiation by gravitational potentials along the line of sight carry with them information on the matter distribution, neutrino masses, and dark energy properties. We examine the constraints that Planck, PolarBear, and CMBpol future data, including from the B-mode polarization or the lensing potential, will be able to place on these quantities. We simultaneously fit for neutrino mass and dark energy equation of state including time variation and early dark energy density, and compare the use of polarization power spectra with an optimal quadratic estimator of the lensing. Results are given as a function of systematics level from residual foreground contamination. A realistic CMBpol experiment can effectively constrain the sum of neutrino masses to within 0.05 eV and the fraction of early dark energy to 0.002. We also present a surprisingly simple prescription for calculating dark energy equation of state constraints in combination with supernova distances from JDEM.Comment: 18 pages, 14 figures. Small changes made to match version to be published in Phys. Rev.