Simultaneous confidence bands for Yule-Walker estimators and order selection

Let $\{X_k,k\in{\mathbb{Z}}\}$ be an autoregressive process of order $q$. Various estimators for the order $q$ and the parameters {\bolds \Theta}_q=(\theta_1,...,\theta_q)^T are known; the order is usually determined with Akaike's criterion or related modifications, whereas Yule-Walker, Burger or maximum likelihood estimators are used for the parameters {\bolds\Theta}_q. In this paper, we establish simultaneous confidence bands for the Yule--Walker estimators $\hat{\theta}_i$; more precisely, it is shown that the limiting distribution of ${\max_{1\leq i\leq d_n}}|\hat{\theta}_i-\theta_i|$ is the Gumbel-type distribution $e^{-e^{-z}}$, where $q\in\{0,...,d_n\}$ and $d_n=\mathcal {O}(n^{\delta})$, $\delta >0$. This allows to modify some of the currently used criteria (AIC, BIC, HQC, SIC), but also yields a new class of consistent estimators for the order $q$. These estimators seem to have some potential, since they outperform most of the previously mentioned criteria in a small simulation study. In particular, if some of the parameters $\{\theta_i\}_{1\leq i\leq d_n}$ are zero or close to zero, a significant improvement can be observed. As a byproduct, it is shown that BIC, HQC and SIC are consistent for $q\in\{0,...,d_n\}$ where $d_n=\mathcal {O}(n^{\delta})$.Comment: Published in at http://dx.doi.org/10.1214/11-AOS963 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Relative perturbation bounds with applications to empirical covariance operators

The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and limit theorems. Our framework is very general, allowing for a huge variety of stationary, ergodic sequences, requiring only $p > 4$ moments. One of the key ingredients is a specific separation measure for population eigenvalues, which we call the relative rank. Developing a new algebraic approach for relative perturbations, we show that this relative rank gives rise to necessary and sufficient conditions for our concentration inequalities and limit theorems.Comment: 55 page

Satellite and radar survey of mesoscale convective system development

June 27, 2002.Includes bibliographical references.Sponsored by National Science Foundation under a Graduate Fellowship.Sponsored by National Science Foundation ATM-9900929

Structural anomalies, spin transitions and charge disproportionation in LnCoO3

The diamagnetic-paramagnetic and insulator-metal transitions in LnCoO3 perovskites (Ln = La, Y, rare earths) are reinterpreted and modeled as a two-level excitation process. In distinction to previous models, the present approach can be characterized as a LS-HS-IS (low-high-intermediate spin) scenario. The first level is the local excitation of HS Co3+ species in the LS ground state. The second excitation is based on the interatomic electron transfer between the LS/HS pairs, leading finally to a stabilization of the metallic phase based on IS Co3+. The model parameters have been quantified for Ln = La, Pr and Nd samples using the powder neutron diffraction on the thermal expansion of Co-O bonds, that is associated with the two successive spin transitions. The same model is applied to interpret the magnetic susceptibility of LaCoO3 and YCoO3.Comment: 52.Conference on Magnetism and Magnetic Materials, November 2007, Tamp

ISU Concert Choir

Kemp Recital Hall Sunday Evening February 21, 1993 7:00p.m