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Locally most powerful rank tests for testing randomness and symmetry
Applications of Mathematics, Tome 43 (1998) no. 2, pp. 93-102 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $1\le i \le N$. 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.
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 $1\le i \le N$. 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.
DOI : 10.1023/A:1023258816397
Classification : 62G10
Keywords: locally most powerful rank tests; randomness; symmetry 
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     author = {Ho, Nguyen Van},
     title = {Locally most powerful rank tests for testing randomness and symmetry},
     journal = {Applications of Mathematics},
     pages = {93--102},
     year = {1998},
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Ho, Nguyen Van. Locally most powerful rank tests for testing randomness and symmetry. Applications of Mathematics, Tome 43 (1998) no. 2, pp. 93-102. doi: 10.1023/A:1023258816397

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