High-dimensional multinomial regression models are very useful in practice but receive less research attention than logistic regression models, especially from the perspective of statistical inference. In this work, we analyze the estimation and prediction error of the contrast-based $\ell_1$-penalized multinomial regression model and extend the debiasing method to the multinomial case, which provides a valid confidence interval for each coefficient and $p$-value of the individual hypothesis test. We apply the debiasing method to identify some important predictors in the progression into dementia of different subtypes. Results of intensive simulations show the superiority of the debiasing method compared to some other inference methods.

翻译：高维多项回归模型在实践中非常有用，但相较于逻辑回归模型，特别是在统计推断角度，其受到的关注较少。本研究分析了基于对比方法的$\ell_1$-惩罚多项回归模型的估计误差和预测误差，并将去偏方法推广至多项回归情形，从而为每个系数提供有效的置信区间，并为单个假设检验提供$p$值。我们将该去偏方法应用于识别不同亚型痴呆进展过程中的重要预测因子。大量模拟结果表明，与其他推断方法相比，该去偏方法具有显著优势。