We propose a penalized likelihood approach in hidden Markov models (HMMs) to perform automated variable selection. To account for a potential large number of covariates, which also may be substantially correlated, we consider the elastic net penalty containing LASSO and ridge as special cases. By quadratically approximating the non-differentiable penalty, we ensure that the likelihood can be maximized numerically. The feasibility of our approach is assessed in simulation experiments. As a case study, we examine the ‘hot hand’ effect, whose existence is highly debated in different fields, such as psychology and economics. In the present work, we investigate a potential ‘hot shoe’ effect for the performance of penalty takers in (association) football, where the (latent) states of the HMM serve for the underlying form of a player.

我们提出了隐马尔可夫模型（HMM）中的惩罚似然法来执行自动变量选择。为了说明潜在的大量协变量（也可能基本相关），我们将包含LASSO和山脊的弹性净罚分视为特殊情况。通过二次近似不可微罚分，我们确保可能性可以在数值上最大化。我们的方法的可行性在仿真实验中进行了评估。作为案例研究，我们研究了“热手”效应，这种效应在心理学和经济学等不同领域都受到了激烈的争论。在当前的工作中，我们研究了潜在的“热靴”效应，该效应可能会导致（协会）足球中的点球手表现，其中HMM的（潜在）状态用作球员的基本形式。