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The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen Bansal, Gholamhossein Hamedani, Hans Volkmer
The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen Bansal, Gholamhossein Hamedani, Hans Volkmer
Naveen Bansal
In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X1,X2,…,Xn)(X1,X2,…,Xn) without the assumption of continuity and symmetry for each component XiXi:
P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,
where allαi≥0 are special weights with∑i=1nαi=1.