Nguyen Van Ho, Department of mathematics, Polytechnic Institute of Hanoi, Hanoi, Vietnam
Abstract: Let $X_i$, $1\le i \le N$, be $N$ independent random variables (i.r.v.) with distribution functions (d.f.) $F_i (x,\Theta)$, $1\le i \le N$, respectively, where $\Theta$ is a real parameter. Assume furthermore that $F_i(\cdot,0)=F(\cdot)$ for $1\le i \le N$. \endgraf Let $R=(R_1,\ldots,R_N)$ and $R^+=(R_1^+,\ldots,R_N^+)$ be the rank vectors of $X = (X_1,\ldots,X_N)$ and $|X| = (|X_1|,\ldots,|X_N|)$, respectively, and let $V = (V_1,\ldots,V_N)$ be the sign vector of $X$. The locally most powerful rank tests (LMPRT) $S=S(R)$ and the locally most powerful signed rank tests (LMPSRT) $S=S(R^+,V)$ will be found for testing $\Theta= 0$ against $\Theta>0$ or $\Theta<0$ with $F$ being arbitrary and with $F$ symmetric, respectively.
Keywords: locally most powerful rank tests, randomness, symmetry
Classification (MSC 1991): 62G10
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