论文标题
部分可观测时空混沌系统的无模型预测
Concave likelihood-based regression with finite-support response variables
论文作者
论文摘要
当响应变量具有有限的支持时，我们为基于似然回归建模的统一框架提出了一个统一的框架。在实践中观察到的数据是离散且有限的，我们的工作是由一个事实激发的。所提出的方法假设一个模型，该模型包括先前考虑的，以log-conconcave分布为特殊情况的间隔审核变量。由此产生的log-okelihoodes是凹的，我们用来确定其最大化剂的渐近正态性，因为观察$ n $的数量倾向于无限于固定的参数$ d $的数量，而$ l_1 $ regardized估计器的收敛速率是零食和$ d $ d $ and $ d $ and $ n to $ n $ n to $ / n $ / d $ / d $ / d $ / d $ / d $ / d $ / d $ / d $ / d / d $ / d。我们考虑一种用于计算估计值的牛顿近端近端，并为其收敛提供了理论保证。可能的应用的范围很广，包括但不限于离散时间内的生存分析，评分调查和问卷调查的结果建模，以及更一般而言的间隔审查的回归。在模拟和数据示例中说明了所提出方法的适用性和实用性。
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume a model which includes models previously considered for interval-censored variables with log-concave distributions as special cases. The resulting log-likelihood is concave, which we use to establish asymptotic normality of its maximizer as the number of observations $n$ tends to infinity with the number of parameters $d$ fixed, and rates of convergence of $L_1$-regularized estimators when the true parameter vector is sparse and $d$ and $n$ both tend to infinity with $\log(d) / n \to 0$. We consider an inexact proximal Newton algorithm for computing estimates and give theoretical guarantees for its convergence. The range of possible applications is wide, including but not limited to survival analysis in discrete time, the modeling of outcomes on scored surveys and questionnaires, and, more generally, interval-censored regression. The applicability and usefulness of the proposed methods are illustrated in simulations and data examples.
