JIMO
A selection problem for a constrained linear regression model
Shaoyong Lai Qichang Xie
Journal of Industrial & Management Optimization 2008, 4(4): 757-766 doi: 10.3934/jimo.2008.4.757
Selecting a good estimate for a constricted linear regression model is investigated by using the generalized information criterion. Some asymptotic properties of the selection procedure with the model average technique are established. It is shown that the selection procedure is asymptotically efficient in the sense that a fitted estimate asymptotically obtains the minimum average squared error from a class of model average estimators.
keywords: generalized information criterion Model selection optimality. constrained linear regression model
CPAA
The existence of weak solutions for a generalized Camassa-Holm equation
Shaoyong Lai Qichang Xie Yunxi Guo YongHong Wu
Communications on Pure & Applied Analysis 2011, 10(1): 45-57 doi: 10.3934/cpaa.2011.10.45
A Camassa-Holm type equation containing nonlinear dissipative effect is investigated. A sufficient condition which guarantees the existence of weak solutions of the equation in lower order Sobolev space $H^s$ with $1 \leq s \leq \frac{3}{2}$ is established by using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself.
keywords: high order nonlinear terms pseudoparabolic regularization technique. weak solution Generalized Camassa-Holm equation

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