We establish a large deviation approximation for the density of an arbitrary sequence of random vectors, by assuming several assumptions on the normalized cumulant generating function and its derivatives. We give two statistical applications to illustrate the result, the first one dealing with a vector of independent sample variances and the second one with a Gaussian multiple linear regression model. Numerical comparisons are eventually provided for these two examples.

中文翻译：

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多元密度函数的大偏差逼近

通过对归一化累积量生成函数及其导数进行假设，我们为随机向量的任意序列的密度建立了一个大偏差近似值。我们提供了两个统计应用程序来说明结果，第一个应用程序处理独立样本方差的向量，第二个应用程序使用高斯多元线性回归模型。最终提供了这两个示例的数值比较。