Class of Tests Based on Subsample Quantiles for Two-sample Scale Problem

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v12i130276 ◽

2021 ◽

pp. 20-33

Author(s):

Shashank D. Shindhe ◽

Sharada V. Bhat ◽

Parameshwar V. Pandit

Keyword(s):

General Class ◽

Scale Problem ◽

Distribution Free ◽

U Statistics

A class of distribution-free tests based on U-statistics with its kernel being function of subsample quantiles is proposed for a two-sample scale problem. The proposed class of tests is a general class of tests that includes numerous members which explore information from the tails of the distributions and tests resistant to outliers. This class of tests includes many existing classes of tests as its subclasses. The distribution of the proposed class of tests is derived and its relevance is discussed. One of its members, which is resistant to outliers in -sample is investigated in detail.

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A Note on a New Class of Distribution-Free Tests for the Two-Sample Scale Problem Based on Subsample Medians

Communication in Statistics- Theory and Methods ◽

10.1081/sta-200026632 ◽

2004 ◽

Vol 33 (9) ◽

pp. 2271-2280 ◽

Cited By ~ 2

Author(s):

I. D. Shetty ◽

Parameshwar V. Pandit

Keyword(s):

Scale Problem ◽

Distribution Free ◽

New Class

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A CLASS OF TWO-SAMPLE SCALE TESTS BASED ON U-STATISTICS

International Journal of Research -GRANTHAALAYAH ◽

10.29121/granthaalayah.v7.i9.2019.569 ◽

2019 ◽

Vol 7 (9) ◽

pp. 138-147

Author(s):

Sharada V. Bhat ◽

Shashank D. Shindhe

Keyword(s):

Asymptotic Distribution ◽

Null Distribution ◽

Small Sample ◽

Scale Problem ◽

Empirical Power ◽

Continuous Distributions ◽

Absolutely Continuous ◽

U Statistics ◽

Random Samples ◽

Power Application

A class of tests based on U-statistic is proposed for two-sample scale problem. The U-statistic is function of extremes of subsamples taken from random samples of two absolutely continuous distributions. The asymptotic distribution, null distribution and efficacy of the class of tests are studied. A comparison of its performance with respect to other tests is studied in terms of Pitman ARE and small sample performance through its empirical power. Application of the class of tests is illustrated through an example.

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ON SOME ROBUST ESTIMATORS BASED ON NON-DISTRIBUTION-FREE $ U $ STATISTICS

Bulletin of Mathematical Statistics ◽

10.5109/13040 ◽

1970 ◽

Vol 14 (1/2) ◽

pp. 1-13

Author(s):

Takashi Yanagawa

Keyword(s):

Robust Estimators ◽

Distribution Free ◽

U Statistics

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Distribution-Free Tests for Location-Scale Problem

American Journal of Mathematical and Management Sciences ◽

10.1080/01966324.2000.10737506 ◽

2000 ◽

Vol 20 (1-2) ◽

pp. 171-181

Author(s):

I.D. Shetty ◽

Parameshwar V. Pandit

Keyword(s):

Scale Problem ◽

Distribution Free

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A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2018.3.4-036 ◽

2018 ◽

Vol 3 (4) ◽

pp. 498-512

Author(s):

Manish Goyal ◽

Narinder Kumar

Keyword(s):

General Class ◽

Null Distribution ◽

Location Parameter ◽

Asymptotic Relative Efficiency ◽

Engineering Economics ◽

U Statistics ◽

Increase With Increase ◽

Location Parameters ◽

Umbrella Alternatives ◽

Testing Homogeneity

In this paper, a general class of non-parametric tests for testing homogeneity of location parameter against umbrella alternatives is proposed. Testing for umbrella alternatives has many applications in the field of biology, medicine, botany, dose level testing, engineering, economics, psychology, zoology. As an example, the effectiveness of a drug is likely to increase with increase of dose up to a certain level and then its effect begins to decrease. The proposed test is based on linear combination of two-sample U-statistics. The null distribution of the test statistics is developed. We compare the test with some other competing tests in terms of Pitman asymptotic relative efficiency. To see execution of the test, a numerical example is provided. Simulation study is carried out to assess the power of proposed class of tests.

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