• Journal of Korean Society for Quality Management
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• v.21 no.2
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• pp.179-193
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• 1993

Modifications of t he weighted Mack-Wolfe tests are proposed for both cases when the peak of umbrella is known and unknown. The modified weighted Mack-Wolfe tests are exactly distribution-free when the continuous populations have the same shape. For the case of peak-known umbrella alternatives, the modified weighted Mack-Wolfe tests remain asymptotically distribution-free when the continuous populations are symmetric, but not necessarily with the same shape. For the case of peak-unknown umbrella alternatives, the maximum of standardized modified weighted Mack-Wolfe tests with peak-known umbrella alternatives was used. The simulation results show that the modified weighted Mack-Wolfe tests are more recommended than the modified Mack-Wolfe tests for various patterns.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1181-1189
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• 2015

The treatment effect in clinical tests depending on dose of the drug; however, it can show a decreasing trend in fixed dose level due to side effects. The trend is known as an umbrella pattern; in addition, the method for the umbrella alternative is quite useful when the tendency is predicted in advance. In this paper, we propose a nonparametric method of umbrella alternatives for a one-way layout by using linear placement described in Orban and Wolfe (1982). The Monte Carlo simulation is adapted to compare the power of proposed procedure with previous methods.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.395-406
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• 2001

In this paper, we propose the test statistic for the umbrella alternatives on c-samples ranked set samples(RSS), where the peak of the umbrella is known. We obtain the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to U-statistic based on simple random samples(SRS). From the simulation work, we compare the empirical powers of the proposed test statistic with U-statistic based on SRS.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.159-171
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• 1994

Some rank score tests are proposed for testing the equality of all sampling distribution functions against umbrella location-scale alternatives in k-sample problem. Only the case of known peak $\ell$ is considered. Under the null hypothesis and a contiguous sequence of unbrella location-scale alternatives, the asymptotic properties of the proposed test statistics are investigated. Also, the asymptotic local powers are compared with each others. The results show that the tests based on the Chen-Wolfe rank analogue statistic are more powerful than others for unequally spaced umbrella location-scale alternatives and robust.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1399-1409
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• 2016

Nonparametric methods in randomized block design were suggested by Friedman (1937) for general alternatives and were also proposed by Page (1963) for ordered alternatives in one-way layout; in addition, K-sample rank tests for umbrella alternatives were suggested by Mack and Wolfe (1981). In this paper, we proposed a nonparametric method of umbrella alternatives for randomized block design using the aligned method proposed by Hodges and Lehmann (1962) to use block information and using placement suggested by Kim (1999). Monte Carlo simulation was also adapted to compare the power of the proposed procedure with previous methods.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1401-1408
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• 2013

Kim and Kim (1992) proposed typical nonparametric method for umbrella alternative in randomized block design with replications. In this paper, We consider a test procedure for umbrella alternatives in a randomized block design using extension of the two sample placement tests described in Orban and Wolfe (1982) and treatment tests described in Kim (1999). We perform a Monte Carlo study to compare the empirical powers of the test statistics for underlying distributions.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.19-34
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• 1994

In this paper we propose nonparametric tests of parallelism against umbrella alternatives of slopes in k-regression lines and investigate the asymptotic properties of the proposed test statistics. For the known peak and unknown peak, we suggest the test statistics and show that, from Monte Carlo study, the proposed test statistics have good empirical powers for heavy tailed distributions than the likelihood ratio tests.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.139-152
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• 1996

In this paper we propose nonparametric tests using optimal weights for umbrella alternatives in a randomized block design. We obtain the optimal weights by maximizing the asymptotic relative efficiency of the proposed test statistics with respect to Mack and Wolf(1981) type test statistic, and investigate asymptotic relative efficiencies of the proposed test statistics using these optimal weights relative to Mack and Wolfe type statistics and linear rank statistic. Throughout simulations for small samples, the proposed test statistic has good powers rather than the other two tests when the block sizes are different.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.105-117
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• 1995

An asymptotically distribution-free procedure is proposed for paralleism of k regression lines against umbrella alternatives. Asymptotic properties are discussed, and comparative results relative to Kim and Lim(1994)'s tests show that our procedure is generally more powerful.

• The Korean Journal of Applied Statistics
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• v.5 no.1
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• pp.41-57
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• 1992

Distribution-free test for umbrella alternatives in a randomized block design is proposed and asymptotic properties test statistics and the asymptotic relatives efficiency (ARE) of the proposed test statistics with respect to the Puri's parametric method are investigated. For given peak points 2,3,4, with 4 blocks and 5 treatments, and with 3 blocks and 5 treatments : for given peak point 3, with 2 blocks and 4 treatments : from the small sample Monte Carlo Study, the empirical powers between the proposed test and Puri's test are compared. Throughout the simulation results, the proposed test statistic is efficient for the heavy tailed distributions.