This paper develops a novel non-parametric test for testing the high-dimensional alpha in linear asset pricing models, where the number of securities can be much larger than the time-dimension of the return series. The asymptotic null distribution and the local power property are established for a class of weighted spatial-sign tests, which results in an optimal test INST by choosing the weight function as the inverse of the norm. The INST test is optimal in the sense that it is locally most powerful within this class. As a non-parametric test, the INST test is also robust to the departures from normality of the error distribution. Monte Carlo simulation and empirical study with real financial data show the superiority of INST test in terms of both robustness and efficiency.

中文翻译：

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线性资产定价模型的高维非参数检验

本文开发了一种新颖的非参数测试，用于测试线性资产定价模型中的高维 alpha，其中证券的数量可以远大于回报序列的时间维度。为一类加权空间符号测试建立了渐近零分布和局部幂特性，通过选择权重函数作为范数的倒数得到最优测试 INST。INST 测试是最佳的，因为它在该类中是局部最强大的。作为非参数检验，INST 检验对于偏离正态分布的误差也具有鲁棒性。蒙特卡洛模拟和真实金融数据的实证研究表明 INST 检验在稳健性和效率方面的优越性。