Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon g−2g-2

We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was mistaken.Comment: 2 page

Nonequilibrium identities of granular vibrating beds

We derive the integral fluctuation theorem around a nonequilibrium stationary state for frictionless and soft core granular particles under an external vibration achieved by a balance between an external vibration and inelastic collisions. We also discuss the connection between the integral fluctuation theorem and the generalized Green-Kubo formula.Comment: 15 pages, no figures to be published in Comptes rendus - M\'ecanique as Proceedings of EuroMech2012 at Graz, Austri

Generalized Green-Kubo formula for a dissipative quantum system

A generalized Green-Kubo formula is derived for a quantum dissipative system of driven Brownian particle, in which the coupling between the system and the environment is linear. The structure is essentially the same as that for the generalized Green-Kubo formula for driven granular particles. It is demonstrated that the correction to the conventional Green-Kubo formula is zero for a free Brownian particle.Comment: 12 pages, no figures. Prog. Theor. Phys. Suppl. (to be published

A Note on Bias in First-Differenced AR(1) Models

In this note, we derive the finite sample bias of the modified ordinary least squares (MOLS) estimator, which was suggested by Wansbeek and Knaap (1999) and reconsidered by Hayakawa (2006a,b). From the formula for the finite sample bias, we find that the bias of the MOLS estimator becomes small as $\rho$, the autoregressive parameter, approaches unity. Simulation results indicate that the MOLS estimator has very small bias and that its empirical size is close to the nominal one.

Small Sample Bias Propreties of the System GMM Estimator in Dynamic Panel Data Models

This paper examines analytically and experimentally why the system GMM estimator in dynamic panel data models is less biased than the first differencing or the level estimators even though the former uses more instruments. We find that the bias of the system GMM estimator is a weighted sum of the biases in opposite directions of the first differencing and the level estimator. We also find that an important condition for the system GMM estimator to have small bias is that the variances of the individual effects and the disturbances are almost of the same magnitude. If the variance of individual effects is much larger than that of disturbances, then all GMM estimators are heavily biased. To reduce such biases, we propose bias-corrected GMM estimators. On the other hand, if the variance of individual effects is smaller than that of disturbances, the system estimator has a more severe downward bias than the level estimator.