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Penalized methods are applied to quasi likelihood analysis for stochasticdifferential equation models. In this paper, we treat the quasi likelihoodfunction and the associated statistical random field for which a polynomialtype large deviation inequality holds. Then penalty terms do not disturb apolynomial type large deviation inequality. This property ensures theconvergence of moments of the associated estimator which plays an importantrole to evaluate the upper bound of the probability that model selection isincorrect.

Penalized quasi likelihood estimation for variable selection