We evaluate the validity of a projection‐based test checking linear models when the number of covariates tends to infinity, and analyze two gene expression datasets. We show that the test is still consistent and derive the asymptotic distributions under the null and alternative hypotheses. The asymptotic properties are almost the same as those when the number of covariates is fixed as long as p/n → 0 with additional mild assumptions. The test dramatically gains dimension reduction, and its numerical performance is remarkable.

中文翻译：

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一个简单而强大的测试，用于评估高维线性模型的拟合优度

当协变量的数量趋于无穷大时，我们评估基于投影的检验线性模型的有效性，并分析两个基因表达数据集。我们证明了检验仍然是一致的，并且在原假设和替代假设下得出了渐近分布。渐近性质几乎与当协变量的数目固定为p / n  →0且具有附加的温和假设时的性质相同。该测试显着提高了尺寸，并且其数值性能非常出色。