Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.Comment: Published at http://dx.doi.org/10.1214/009053604000000021 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Contributors to JAEPL, Vol. 27

Contributor

Measuring q_0 from the Distortion of Voids in Redshift Space

Because the transformation from distance to redshift is nonlinear, maps in redshift space become increasingly distorted as the redshift z becomes greater. As noted by Alcock \& Paczy\'nski (1979), observed redshift distortions can be used to estimate the deceleration parameter $q_0$. If $q_0$ is greater than -1, voids in redshift space will be elongated along the line of sight. In addition, distant voids will have a greater volume in redshift space than nearby voids. Accurate measurement of the volume and the axis ratio of voids, as a function of their central redshift, will provide an estimate of $q_0$. To test this method of estimating $q_0$, I create a two-dimensional toy universe, free of peculiar velocities, in which the galaxies are located near the walls of Voronoi cells. The galaxies are then mapped into redshift space, adopting different values of $q_0$. In redshift space, I estimate the area and the axis ratio of the voids by fitting ellipses within the voids, using an algorithm which maximizes the area of the empty ellipses and ensures that ellipses do not overlap. The accuracy of the estimated values of $q_0$ is limited by the intrinsic scatter in the size and shape of the voids. In the toy universe, distinguishing between a $q_0 = -1$ universe and a $q_0 = 1/2$ universe requires a survey which goes to a depth z > 0.1 in redshift space. Peculiar velocities will create an additional source of uncertainty for the values of $q_0$ measured in N-body simulations and in the real universe.Comment: to appear in the ApJ. 14 pages uuencoded compressed postscript Seven figures available as a compressed tar file via ftp at ftp://bessel.mps.ohio-state.edu/pub/ryden/figs.tar.

Corporal Pedagogies: An Introduction

Essays in this section address the question: “What happens when we understand teaching and learning as bodily arts that holistically engage us rather than disconnect us from our embodied selves?

Swamps, Flat Earthers, and Boughs of Holly: “Encountering” the Natural World and the Poetics of Environmental Literacy

Encountering” the Natural World and the Poetics of Environmental Literac