Locally most powerful rank tests for testing randomness and symmetry

Nguyen Van Ho

Applications of Mathematics (1998)

  • Volume: 43, Issue: 2, page 93-102
  • ISSN: 0862-7940

Abstract

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Let X i , 1 ≤ i ≤ N , be N independent random variables (i.r.v.) with distribution functions (d.f.) F i ( x , Θ ) , 1 ≤ i ≤ N , respectively, where Θ is a real parameter. Assume furthermore that F i ( · , 0 ) = F ( · ) for 1 ≤ i ≤ N . Let R = ( R 1 , ... , R N ) and R + = ( R 1 + , ... , R N + ) be the rank vectors of X = ( X 1 , ... , X N ) and | X | = ( | X 1 | , ... , | X N | ) , respectively, and let V = ( V 1 , ... , 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 Θ = 0 against Θ > 0 or Θ < 0 with F being arbitrary and with F symmetric, respectively.

How to cite

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Ho, Nguyen Van. "Locally most powerful rank tests for testing randomness and symmetry." Applications of Mathematics 43.2 (1998): 93-102. <http://eudml.org/doc/32999>.

@article{Ho1998,
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 $1\le i \le N$. 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.},
author = {Ho, Nguyen Van},
journal = {Applications of Mathematics},
keywords = {locally most powerful rank tests; randomness; symmetry; locally most powerful rank tests; randomness; symmetry},
language = {eng},
number = {2},
pages = {93-102},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Locally most powerful rank tests for testing randomness and symmetry},
url = {http://eudml.org/doc/32999},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Ho, Nguyen Van
TI - Locally most powerful rank tests for testing randomness and symmetry
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 2
SP - 93
EP - 102
AB - 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.
LA - eng
KW - locally most powerful rank tests; randomness; symmetry; locally most powerful rank tests; randomness; symmetry
UR - http://eudml.org/doc/32999
ER -

References

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  1. 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. (1964) MR0174120
  2. A course in nonparametric statistics, Holden-Day, New York, 1969. (1969) MR0246467
  3. Theory of Rank Tests, Academia, Praha, 1967. (1967) MR0229351
  4. The locally most powerful rank tests, Acta Mathematica Vietnamica, T3, N1 (1978), 14–23. (1978) 
  5. The power of rank tests, AMS 24 (1953), 23–43. (1953) Zbl0050.14702MR0054208
  6. A useful convergence theorem for probability distributions, AMS 18 (1947), 434–438. (1947) MR0021585

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