Valid Asymptotic Expansions for the Maximum Likelihood Estimator of the Parameter of a Stationary, Gaussian, Strongly Dependent Process

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin's (1980) general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood derivatives; (ii) appeal to a simple result of Skovgaard (1986) to obtain from this an Edgeworth expansion for the joint distribution of the log-likelihood derivatives; (iii) appeal to and extension of arguments of Bhattacharya and Ghosh (1978) to accomplish the passage from the result on the log-likelihood derivatives to the result for the maximum likelihood estimators. We develop and make extensive use of a uniform version of Dahlhaus's (1989) Theorem 5.1 on products of Toeplitz matrices; the extension of Dahlhaus's result is of interest in its own right. A small numerical study of the efficacy of the Edgeworth expansion is presented for the case of fractional Gaussian noise.Edgeworth expansions, long memory processes, ARFIMA models

A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

Supersymmetric Brane World Scenarios from Off-Shell Supergravity

Using N=2 off-shell supergravity in five dimensions, we supersymmetrize the brane world scenario of Randall and Sundrum. We extend their construction to include supersymmetric matter at the fixpoints.Comment: 15 pages, no figures, late

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

Leo V: A Companion of a Companion of the Milky Way Galaxy

We report the discovery of a new Milky Way dwarf spheroidal galaxy in the constellation of Leo identified in data from the Sloan Digital Sky Survey. Leo V lies at a distance of about 180 kpc, and is separated by about 3 degrees from another recent discovery, Leo IV. We present follow-up imaging from the Isaac Newton Telescope and spectroscopy from the Hectochelle fiber spectrograph at the Multiple Mirror Telescope. Leo V's heliocentric velocity is 173.4 km/s, which is offset by about 40 km/s from that of Leo IV. A simple interpretation of the kinematic data is that both objects may lie on the same stream, though the implied orbit is only modestly eccentric (e = 0.2)Comment: Submitted to ApJ (Letters