Filing for the Union Army Pension: A Summary from Historical Evidence

pension; application; claim; surgeon's certificates

Strong Stability of Nash Equilibria in Load Balancing Games

We study strong stability of Nash equilibria in load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an NE approximates an SNE. Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre- and post-deviation costs. An NE is said to be a r-approximate SNE (r >= 1) if there is no coalition of jobs such that each job of the coalition will have an IR more than r from coordinated deviations of the coalition. While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5/4)-approximate SNE, which together with the lower bound already established in the literature yields a tight approximation bound. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in load balancing games. To establish our upper bound, we make a novel use of a graph-theoretic tool.Comment: 17 pages and 4 figure

High dimensional generalized empirical likelihood for moment restrictions with dependent data

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment restrictions, as well as the degree of data dependence. It is shown that even in the high dimensional time series setting, the GEL ratio can still behave like a chi-square random variable asymptotically. A consistent test for the over-identification is proposed. A penalized GEL method is also provided for estimation under sparsity setting

Semiparametric Estimation of Heteroscedastic Binary Sample Selection Model

Binary choice sample selection models are widely used in applied economics with large cross-sectional data where heteroscedaticity is typically a serious concern. Existing parametric and semiparametric estimators for the binary selection equation and the outcome equation in such models suffer from serious drawbacks in the presence of heteroscedasticity of unknown form in the latent errors. In this paper we propose some new estimators to overcome these drawbacks under a symmetry condition, robust to both nonnormality and general heterscedasticity. The estimators are shown to be $\sqrt{n}$-consistent and asymptotically normal. We also indicate that our approaches may be extended to other important models.

Two sample tests for high-dimensional covariance matrices

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the "large $p$, small $n$" situations and (ii) without assuming parametric distributions for the two populations. These two aspects surpass the capability of the conventional likelihood ratio test. The proposed tests can be used to test on covariances associated with gene ontology terms.Comment: Published in at http://dx.doi.org/10.1214/12-AOS993 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org