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Full-Text Articles in Statistics and Probability

Obtaining Critical Values For Test Of Markov Regime Switching, Douglas G. Steigerwald, Valerie Bostwick Oct 2012

Obtaining Critical Values For Test Of Markov Regime Switching, Douglas G. Steigerwald, Valerie Bostwick

Douglas G. Steigerwald

For Markov regime-switching models, testing for the possible presence of more than one regime requires the use of a non-standard test statistic. Carter and Steigerwald (forthcoming, Journal of Econometric Methods) derive in detail the analytic steps needed to implement the test ofMarkov regime-switching proposed by Cho and White (2007, Econometrica). We summarize the implementation steps and address the computational issues that arise. A new command to compute regime-switching critical values, rscv, is introduced and presented in the context of empirical research.


Big Data And The Future, Sherri Rose Jul 2012

Big Data And The Future, Sherri Rose

Sherri Rose

No abstract provided.


Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell Apr 2012

Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell

Mark R Segal

We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized …


Backcalculation Of Hiv Infection Rates, Peter Bacchetti, Mark Segal, Nicholas Jewell Apr 2012

Backcalculation Of Hiv Infection Rates, Peter Bacchetti, Mark Segal, Nicholas Jewell

Mark R Segal

Backcalculation is an important method of reconstructing past rates of human immunodeficiency virus (HIV) infection and for estimating current prevalence of HIV infection and future incidence of acquired immunodeficiency syndrome (AIDS). This paper reviews the backcalculation techniques, focusing on the key assumptions of the method, including the necessary information regarding incubation, reporting delay, and models for the infection curve. A summary is given of the extent to which the appropriate external information is available and whether checks of the relevant assumptions are possible through use of data on AIDS incidence from surveillance systems. A likelihood approach to backcalculation is described …


Loss Function Based Ranking In Two-Stage, Hierarchical Models, Rongheng Lin, Thomas A. Louis, Susan M. Paddock, Greg Ridgeway Mar 2012

Loss Function Based Ranking In Two-Stage, Hierarchical Models, Rongheng Lin, Thomas A. Louis, Susan M. Paddock, Greg Ridgeway

Rongheng Lin

Several authors have studied the performance of optimal, squared error loss (SEL) estimated ranks. Though these are effective, in many applications interest focuses on identifying the relatively good (e.g., in the upper 10%) or relatively poor performers. We construct loss functions that address this goal and evaluate candidate rank estimates, some of which optimize specific loss functions. We study performance for a fully parametric hierarchical model with a Gaussian prior and Gaussian sampling distributions, evaluating performance for several loss functions. Results show that though SEL-optimal ranks and percentiles do not specifically focus on classifying with respect to a percentile cut …


Testing For Regime Swtiching: A Comment, Douglas Steigerwald, Andrew Carter Dec 2011

Testing For Regime Swtiching: A Comment, Douglas Steigerwald, Andrew Carter

Douglas G. Steigerwald

An autoregressive model with Markov-regime switching is analyzed that reflects on the properties of the quasi-likelihood ratio test developed by Cho and White (2007). For such a model, we show that consistency of the quasi-maximum likelihood estimator for the population parameter values, on which consistency of the test is based, does not hold. We describe a condition that ensures consistency of the estimator and discuss the consistency of the test in the absence of consistency of the estimator.


Some Non-Asymptotic Properties Of Parametric Bootstrap P-Values, Chris Lloyd Dec 2011

Some Non-Asymptotic Properties Of Parametric Bootstrap P-Values, Chris Lloyd

Chris J. Lloyd

The bootstrap P-value is the exact tail probability of a test statistic, cal-culated assuming the nuisance parameter equals the null maximum likelihood (ML) estimate. For discrete data, bootstrap P-values perform amazingly well even for small samples, even as standard first order methods perform surprisingly poorly. Why is this? Detailed numerical calculations in Lloyd (2012a) strongly suggest that the good performance of bootstrap is not explained by asymptotics. In this paper, I establish several desirable non-asymptotic properties of bootstrap P-values. The most important of these is that bootstrap will correct ‘bad’ ordering of the sample space which leads to a more …