Estimation of Time-Varying Parameters in Statistical Models: An Optimization Approach
Estimation of Time-Varying Parameters in Statistical Models: An Optimization Approach
复制标题
统计模型中时变参数的估计：一种优化方法
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Tsitsiklis
中科院分区：
文献类型：
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作者：
D. Bertsimas;D. Gamarnik;J. Tsitsiklis
当潜在回归函数是利普希茨连续时，我们提出一种凸优化方法来解决非参数回归估计问题。这种方法基于最小化经验平方误差之和，并受利普希茨连续性所隐含的约束条件限制。由此产生的优化问题具有凸目标函数和线性约束，因此可以高效求解。当样本量趋于无穷大时，通过这种技术计算出的估计函数被证明几乎必然一致收敛于潜在回归函数，从而提供了一种非常强的一致性形式。我们还针对统计模型中未知参数的最大似然估计提出一种凸优化方法，其中参数连续依赖于一些可观测的输入变量。对于许多经典分布形式，基础优化问题中的目标函数是凸的，约束是线性的。因此，这些问题也可以高效求解。
We propose a convex optimization approach to solving the nonparametric regression estimation problem when the underlying regression function is Lipschitz continuous. This approach is based on the minimization of the sum of empirical squared errors, subject to the constraints implied by Lipschitz continuity. The resulting optimization problem has a convex objective function and linear constraints, and as a result, is efficiently solvable. The estimated function computed by this technique, is proven to convergeto the underlying regression function uniformly and almost surely, when the sample size grows to infinity, thus providing a very strong form of consistency. Wealso propose a convex optimization approach to the maximum likelihood estimation of unknown parameters in statistical models, where the parameters depend continuously on some observable input variables. For a number of classical distributional forms, the objective function in the underlying optimization problem is convex and the constraints are linear. These problems are, therefore, also efficiently solvable.