提出基于核方法的非参数检验框架，验证金融模型中的形状约束。
Kernel-Based Nonparametric Tests For Shape Constraints
- 先无约束估计，再检验正性、单调性、凸性等经济形状约束。
- 在有限网格上构建联合沃尔德统计量，实现对形状假设的严格检验。
- 算法高效可扩展，适用于大规模数据，适合资产定价等金融场景。
我们提出一种基于核的非参数框架，用于均值-方差优化，能够对金融中具有经济意义的形状约束（如正性、单调性、凸性）进行推断。金融计量中的许多核心假设自然表现为潜在函数（如期限溢价、CAPM关系、定价核）上的形状关系，但在估计过程中强制施加这些约束可能掩盖真实的经济偏差；因此，本方法通过先估计无约束解，再进行形状性质检验，实现学习与验证分离。我们建立了正则化样本估计器的统计性质，包括渐近一致性、泛函中心极限定理，以及达到蒙特卡洛速率的有限样本偏差界（仅含正则化项）。基于此结果，我们构造了在有限网格上检验形状约束的联合沃尔德统计量。一个基于枢轴化乔列斯基分解的高效算法使该方法可扩展至大规模数据集。数值实验，包括基于期权的资产定价应用，展示了该方法在评估单调性和凸性限制方面的实用性。
原文摘要 · Abstract (English)
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in financial econometrics are naturally expressed as shape relations on latent functions (e.g., term premia, CAPM relations, and the pricing kernel), yet enforcing such constraints during estimation can mask economically meaningful violations; our approach therefore separates learning from validation by first estimating an unconstrained solution and then testing shape properties. We establish statistical properties of the regularized sample estimator and derive rigorous guarantees, including asymptotic consistency, a functional central limit theorem, and a finite-sample deviation bound achieving the Monte Carlo rate up to a regularization term. Building on these results, we construct a joint Wald-type statistic to test shape constraints on finite grids. An efficient algorithm based on a pivoted Cholesky factorization yields scalability to large datasets. Numerical studies, including an options-based asset-pricing application, illustrate the usefulness of the proposed method for evaluating monotonicity and convexity restrictions.
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