Explicit bounds on Levy–Prohorov distance for a class of multidimensional distribution functions

✍ Scribed by Isha Dewan; B.L.S.Prakasa Rao

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 144 KB
• Volume: 48
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00179-0

✦ Synopsis

Let F(x1; : : : ; x k ) and G(x1; : : : ; x k ) = FX 1 (x1) : : : FX k (x k ), where FX i (xi); 16i6k, are the one-dimensional marginal distributions of F, be two distribution functions on R k . Here, we obtain explicit bounds for the Levy-Prohorov distance between F and G using some general results due to Yurinskii (1975, Theory Probab. Appl. 20, 1-10).