A Two-Sample Adaptive Distribution-Free Test

Hogg, Robert V.; Fisher, Doris M.; Randles, Ronald H.

doi:10.2307/2285950

Cited by 83 publications

(24 citation statements)

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“…The second is to partition the sample space and use a different test statistic in each set of the partition to construct a rejection region. This was originally proposed by Hogg, Fisher and Randles [7]. See [14] for more results along this research line.…”

Section: Remarkmentioning

confidence: 93%

“…The third is the proposed here that generates two partitions: one in the sample space and one in the alternative, and constructs a level-α acceptance region of Θ iA in each set of the former partition. To see the difference between the second and the third, Hogg, Fisher and Randles [7] define a region R i ⊂ S, instead of R i ⊂ S i as we propose, for (2.1) satisfying sup…”

Section: Remarkmentioning

confidence: 99%

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On hypothesis testing with a partitioned random alternative

Wang

2010

Sci. China Math.

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It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on distributions. When m = 1, it is done by the (traditional) hypothesis test. In this paper, a generalization to the case m > 1 is proposed. The fundamental difference with the case m = 1 is that the new alternative hypothesis is a partition of m multiple claims and is data-dependent. Data is used to decide which claim in the partition is to be tested as the alternative. Thus, a random alternative is involved. The conditional and overall type I errors of the proposed test are controlled at a given level, and this test can be used as a new solution for the general multiple test problem. Several classical problems, including the one-sample problem, model selection in multiple linear regression, and multi-factor analysis, are revisited, and new tests are provided correspondingly. Consequently, the famous two-sided t-test should be replaced by the proposed.

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Section: Remarkmentioning

confidence: 93%

Section: Remarkmentioning

confidence: 99%

On hypothesis testing with a partitioned random alternative

Wang

2010

Sci. China Math.

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“…Gastwirth (1965) considered modifications of traditional Wilcoxon rank-sum statistic for asymmetric distributions which led to the development of HFR statistic in Hogg, Fisher, and Randles (1975). Over the years, such a statistic has been widely used in statistical literature; see for example, Kössler (1996), Neuhäuser, Büning, andHothorn (2004), Kössler (2010), Thas et al (2012) among others.…”

Section: Please Scroll Down For Articlementioning

confidence: 99%

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

Mukherjee

Sen

2015

International Journal of Production Research

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The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg-Fisher-Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.

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“…Note, in our context, choosing a value of c amounts to choosing a score that leads to a specific nonparametric test. For rank tests, the general problem of choosing a score was first adressed and tackled by Hajek and Sidak (1967) and later by Hajek (1969Hajek ( , 1970, Hogg et al (1975). A good review is given in Sidak et al (1999).…”

Section: Choice Of C: Some Suggestionsmentioning

confidence: 99%

“…Thus an optimum choice of c irrespective of different configurations of r, s and n does not exist. On the other hand, for a given choice of r, s and n and a given alternative, the performance of the test would depend on the shape of the parent distribution (see Sidak et al 1999;Hajek 1969Hajek , 1970Hogg et al 1975;Banerjee 1986, 1991). Hajek (1969Hajek ( , 1970, in particular, showed that change in tail weights of the unknown parent distribution significantly affects the optimum choice of the score.…”

Section: Choice Of C: Some Suggestionsmentioning

confidence: 99%