Yichen Feng, Jean-Pierre Fouque, Tomoyuki Ichiba
Department of Statistics and Applied Probability, South Hall, University of California, Santa Barbara, CA 93106, USA.
Abstract: We study linear-quadratic stochastic differential games on directed chains inspired by the directed chain stochastic differential equations introduced by Detering, Fouque and Ichiba. We solve explicitly for Nash equilibria with a finite number of players and we study more general finite-player games with a mixture of both directed chain interaction and mean field interaction. We investigate and compare the corresponding games in the limit when the number of players tends to infinity. The limit is characterized by Catalan functions and the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain, with or without the presence of mean field interaction.
Keywords: Linear-quadratic stochastic games, directed chain network, Nash equilibrium, Catalan functions, Catalan Markov chain, mean field games.
Pages: 25 – 67 | Full PDF Paper
1. School of Public Health, University of Alberta, Edmonton, Canada.
2. Department of Medicine, University of Calgary, Calgary, Canada.
Abstract: Stepwise covariate selection is a popular method for multivariable regression model building. Based on the different significance levels pre-specified by statisticians, different covariates are included in the model. Further analyses with these models might introduce biases. This paper proposes a novel method to select covariates for stepwise logistic regression without pre-setting a significance level. Multiple models containing different numbers of covariates were outputted for final model selection. A user-oriented SAS macro was developed. Users of the macro may determine the final models, based on estimated characteristic changes of the overall models, the variances of the covariate effects on the response variable and their special needs. With this method, model selections are much easier than with purposeful or the best subsets method. This method improved stepwise covariate selection processes. Broad applications are expected.
Keywords: logistic regression, model building, multivariate statistics, SAS Programming, Statistical computation.
Pages: 68 – 78 | Full PDF Paper