High‐dimensional non‐parametric tests for linear asset pricing models

Abstract

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.