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参数位于参数空间边界时的惩罚准似然估计与模型选择AI 解读

Summary We consider here penalized likelihood-based estimation and model selection applied to econometric time series models, which allow for nonnegativity (boundary) constraints on some or all of the parameters. We establish that joint model selection and estimation result in standard asymptotic Gaussian distributed estimators. The results contrast with nonpenalized estimation, which, as is well-known, leads to nonstandard asymptotic distributions that depend on the unknown…

参数空间边界上的 Bootstrap 推断及条件波动率应用AI 解读

It is a well-established fact that – with an unknown number of nuisance parameters at the boundary – testing a null hypothesis on the boundary of the parameter space is infeasible in practice as the limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of…