Data-Driven Tests for Trend

Wyłupek, Grzegorz

doi:10.1080/03610926.2012.697967

Cited by 2 publications

(8 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a result, the considered problem is fully non‐parametric. Furthermore, such a formulation satisfies the postulates emphasized by Terpstra & Magel () and strengthened by Wyłupek (), which can be paraphrased as follows: the errors of both kinds of a good test ‘should decrease as the sample sizes are growing’. Obviously, the faster the errors decrease the better the test is.…”

Section: Introductionmentioning

confidence: 74%

“…We reject the hypothesis

{scriptℋ}_{u}^{[l, h]} (j)

for its large values. For more comments on the aforementioned objects, see Ledwina & Wyłupek (, b) and Wyłupek ().…”

Section: The New Test Statisticmentioning

confidence: 99%

“…The reason is that the solution proposed by them is analogical to the test proposed by Terpstra & Magel () dedicated to detection of the increasing trend

{scriptA}_{+} : F_{1} \geq \dots \geq F_{k}, F_{i} \neq F_{j} for some 1 \leq i < j \leq k,

under the assumption of the simple shift model. In spite of the fact that the Terpstra & Magel's () test takes care of the control of the power function outside the alternative

{scriptA}_{+}

, it often leads to the completely misleading inference, what has been noticed by Wyłupek (), see Table 6, p. 1422.…”

Section: Introductionmentioning

confidence: 99%

“…In order to create a test which satisfies this condition, we base on some ideas contained in the work of Ledwina & Wyłupek (,b) and Wyłupek (). In particular, to construct a test statistic in the problem

({scriptℋ}_{u}, {scriptA}_{u})

, we exploit some two‐sample statistics elaborated there.…”

Section: Introductionmentioning

confidence: 99%

“…However, the idea behind the form of the final test statistic is different here. Moreover, it leads to even better results than a simple adaptation of the test proposed in Wyłupek (). Thereby, the new solution also improves upon the ibidem procedure in the case when p = k .…”

Section: Introductionmentioning

confidence: 99%

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An Automatic Test for the Umbrella Alternatives

Wyłupek

2016

Scandinavian J Statistics

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The paper proposes a new test for detecting the umbrella pattern under a general non-parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level˛on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.

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Section: Introductionmentioning

confidence: 74%

“…We reject the hypothesis

{scriptℋ}_{u}^{[l, h]} (j)

for its large values. For more comments on the aforementioned objects, see Ledwina & Wyłupek (, b) and Wyłupek ().…”

Section: The New Test Statisticmentioning

confidence: 99%

“…The reason is that the solution proposed by them is analogical to the test proposed by Terpstra & Magel () dedicated to detection of the increasing trend

{scriptA}_{+} : F_{1} \geq \dots \geq F_{k}, F_{i} \neq F_{j} for some 1 \leq i < j \leq k,

under the assumption of the simple shift model. In spite of the fact that the Terpstra & Magel's () test takes care of the control of the power function outside the alternative

{scriptA}_{+}

, it often leads to the completely misleading inference, what has been noticed by Wyłupek (), see Table 6, p. 1422.…”

Section: Introductionmentioning

confidence: 99%

({scriptℋ}_{u}, {scriptA}_{u})

, we exploit some two‐sample statistics elaborated there.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Automatic Test for the Umbrella Alternatives

Wyłupek

2016

Scandinavian J Statistics

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ODC and ROC Curves, Comparison Curves and Stochastic Dominance

Ledwina,

Zagdański

2024

Int Statistical Rev

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SummaryWe discuss two novel approaches to inter‐distributional comparisons in the classical two‐sample problem. Our starting point is properly standardised and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic curves, denoted by ODC and ROC, respectively. The proposed new curves are termed the comparison curves. Their estimates, being weighted rank processes on (0,1), form the basis of inference. These weighted processes are intuitive, well‐suited for visual inspection of data at hand and are also useful for constructing some formal inferential procedures. They can be applied to several variants of two‐sample problem. Their use can help improve some existing procedures both in terms of power and the ability to identify the sources of departures from the postulated model. To simplify interpretation of finite sample results, we restrict attention to values of the processes on a finite grid of points. This results in the so‐called bar plots (B‐plots), which readably summarise the information contained in the data. What is more, we show that B‐plots along with adjusted simultaneous acceptance regions provide principled information about where the model departs from the data. This leads to a framework that facilitates identification of regions with locally significant differences.We show an implementation of the considered techniques to a standard stochastic dominance testing problem. Some min‐type statistics are introduced and investigated. A simulation study compares two tests pertinent to the comparison curves to well‐established tests in the literature and demonstrates the strong and competitive performance of the former in many typical situations. Some real data applications illustrate simplicity and practical usefulness of the proposed approaches. A range of other applications of considered weighted processes is briefly discussed too.

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Data-Driven Tests for Trend

Cited by 2 publications

References 20 publications

An Automatic Test for the Umbrella Alternatives

An Automatic Test for the Umbrella Alternatives

ODC and ROC Curves, Comparison Curves and Stochastic Dominance

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