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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, August 1, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl S.V.  Nagaev}
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\centerline{\bf The best-possible constant in a Berry-Esseen type bound
for a self-normalized statistic}
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Consider the self-normalized statistic

$$T_n  = (X_1 + X_2 +... + X_n ) /( X_1 ^2 + X_2^2 +...X_n^2)^{1/2}$$

where $X_j$ are i.i.d. random variables with $EX_1 = 0$.

It is known that

$$| P( T_n < x ) - P( Y < x )| < cE|X|^3/(EX^2)^{3/2}$$

where Y is a standard normal variable and c is some absolute constant
(Bentkus and Goetze, 1996). I will give an estimate for the best constant c.

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