| Title:
|
Locally most powerful rank tests for testing randomness and symmetry (English) |
| Author:
|
Ho, Nguyen Van |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
93-102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
locally most powerful rank tests |
| Keyword:
|
randomness |
| Keyword:
|
symmetry |
| MSC:
|
62G10 |
| idZBL:
|
Zbl 0953.62044 |
| idMR:
|
MR1609174 |
| DOI:
|
10.1023/A:1023258816397 |
| . |
| Date available:
|
2009-09-22T17:56:59Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134377 |
| . |
| Reference:
|
[1] Gibbons, J.D.: On the power of two-sample rank tests on the quality of two distribution functions.J. Royal Stat. Soc., Series B 26 (1964), 293–304. MR 0174120 |
| Reference:
|
[2] Hájek, J.: A course in nonparametric statistics.Holden-Day, New York, 1969. MR 0246467 |
| Reference:
|
[3] Hájek, J., Šidák, Z.: Theory of Rank Tests.Academia, Praha, 1967. MR 0229351 |
| Reference:
|
[4] Nguyen Van Ho: The locally most powerful rank tests.Acta Mathematica Vietnamica, T3, N1 (1978), 14–23. |
| Reference:
|
[5] Lehmann, E.L.: The power of rank tests.AMS 24 (1953), 23–43. Zbl 0050.14702, MR 0054208 |
| Reference:
|
[6] Scheffé, H.: A useful convergence theorem for probability distributions.AMS 18 (1947), 434–438. MR 0021585 |
| . |
