In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.

This paper proposes a high-capacity reversible watermarking algorithm for medical image analysis based on the difference block histogram, which will benefit the medical image authentication and doctor–patient confidentiality. By dividing the original medical image into blocks, the method displaces the peak point of a block's histogram of difference and embeds multi-bit information at 1 pixel point. In so doing, secret communication and storage of large-capacity invisible medical diagnoses and patients personal confidential data can be achieved. Once the watermark is extracted, not only the image integrity is authenticated, but also the original image and personal data of the patient can be recovered in a nondestructive way. With low computational complexity, a high embedding capacity and little demand for auxiliary information, the proposed algorithm is highly secure and practical.