Some results for $U$-statistics and strong demimartingales
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In this paper, we obtain a result that a $U$-statistic $U_n$ based on associated random variables and a kernel $k(x_1,\ldots,x_m)$ which is a bounded variance function can be written as the difference of two strong demimartingales. Moreover, we establish Chow type minimal inequalities for strong demimartingales and obtain Marshall type minimal inequalities as well as a Value-at-Risk bound for ($\mathop{\min}_{1\leq k \leq n}S_k$).
Abstract
In this paper, we obtain a result that a $U$-statistic $U_n$ based on associated random variables and a kernel $k(x_1,\ldots,x_m)$ which is a bounded variance function can be written as the difference of two strong demimartingales. Moreover, we establish Chow type minimal inequalities for strong demimartingales and obtain Marshall type minimal inequalities as well as a Value-at-Risk bound for ($\mathop{\min}_{1\leq k \leq n}S_k$).
참고문헌 (12)
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