Statistics Colloquia (Winter term 2005)

Department of Mathematics and Statistics

Dalhousie University

Statistics Colloquium Chair: Hong Gu

Unless otherwise indicated, the following location and time apply to all colloquium talks.

Location: Colloquium Room (Chase Building, Room 319)

Time: Thursday 3:30 to 4:30pm.

Date : Jan. 27 3:30 to 4:30pm

Speaker: Chris Field, Dept. of Math. & Stat. , Dalhousie University

Topic : Variable Selection both Practical and Conceptual

Abstract:    
I will first look at issues of variable selection as they arise in longitudinal data analysis. In ongoing work with Eva Cantoni,
Joanna Flemming and Elvezio Ronchetti, have developed variable selection procedures based on estimated prediction error.
Our computations use GEE estimates but other settings are possible.  To compute the prediction error, we use the ideas of
cross validation where the size of the prediction sample grows as the number of experimental units increases. To handle the
cases where the number of variables is large, we use MCMC ideas as developed by Guoqi Qian and me to move through the
model space. The procedure not only gives an estimate of the best model but will also give all models whose prediction error
is within one standard error of the chosen model, as in the spirit of bagging. Will also briefly discuss some unifying ideas of
model selection using the Kullback-Leibler information. Our aim to have a procedure which works when the true model lies
outside the class of models within which we are doing the selection. This is based on ongoing work with Guoqi Qian.

Time : Feb. 3, 3:30 to 4:30pm

Speaker: Ying Zhang, Dept. of Math. & Stat. , Acadia University

Topic : Computer Algebra Derivation of the Bias of Commonly-Used Time Series Estimators

Abstract: 

There are three commonly used linear estimators in the time series analysis: least squares, Burg and Yule Walker estimators. Burg and Yule Walker estimators both use the Durbin-Levinson recursion for fitting the AR(p) model. The Burg algorithm estimates the partial autocorrelation by minimizing a sum of squares of observed forward and backward prediction errors, while Yule-Walker algorithm calculates it recursively using the estimated autocovariances up to lag p. The Burg estimator can be considered as the least-squares estimator constrained by the Durbin-Levinson recursion.

Using computer algebra the biases to O (1/n) of these three estimators in AR(1) and AR(2) models is derived. For the Burg estimator, it is shown the bias to O (1/n) to be equal to that of the least-squares estimates in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the bias of the Burg estimator because this problem is too intractable without using computer algebra. We demonstrate that the Burg estimator is preferable to the least-squares or Yule-Walker estimator.

Time: Feb. 10, 3:30 to 4:30pm

Speaker: Huaichun Wang, Dept. of Math. & Stat. , Dalhousie University

Topic :The effects of DNA compositional bias on genome evolution