Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data

Gaigall, Daniel

doi:10.1007/s00184-019-00742-5

Cited by 5 publications

(7 citation statements)

References 40 publications

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“…is open and convex, compare with Gaigall (2019). While we allow any dependence structure between X j,1 and X j,2 , we like to infer the null hypothesis of marginal homogeneity H : P X j,1 = P X j,2 versus K : P X j,1 = P X j,2 .…”

Section: Testing Marginal Homogeneity In Hilbert Spacesmentioning

confidence: 99%

“…Given that α ∈ (0, 1) is the significance level, neither a (1 − α)-quantile c n,1−α of CvM n nor the (1 − α)-quantile c 1−α of Z is available as critical value in applications. To resolve this problem, we propose the estimation of the quantiles via bootstrapping in the spirit of Efron (1979) and follow the idea in Gaigall (2019), where the usual two-sample Cramér-von-Mises distance is applied to bivariate random vectors with values in R 2 . Note that under the null hypothesis…”

Section: Asymptotic Theory Of the Test Statisticmentioning

confidence: 99%

“…Thus, either way S n p → 0. Our assumptions on the joint distribution of X 1,1 , e i and X 1,2 , e i , i ∈ I , ensure that Assumption 1 and Assumption 2 in Gaigall (2019) are satisfied, and it follows from Theorem 1 and Theorem 3 in Gaigall (2019) that D n (e 1 ) d → S as n → ∞, where S is a real-valued random variable and not constantly zero. In all, from…”

Section: Applications To Stock Market Returnsmentioning

confidence: 99%

“…In contrast with the unpaired setting, exchangeability is not given in general under the null hypothesis of marginal homogeneity. This is already known for bivariate distributions on the Cartesian square of the real line, see Gaigall (2019). For that reason, a permutation test, such as they are used by Hall and Tajvidi (2002) and Bugni and Horowitz (2018) for the unpaired two-sample setting under functional data, or in Bugni and Horowitz (2018) in the more general situation of one control group against several treatment groups, is no option in our situation.…”

Section: Introductionmentioning

confidence: 98%

“…With a view to the consistency of the testing procedure, we apply a test statistic of Cramér-von-Mises type. See Anderson and Darling (1952) and Rosenblatt (1952) for Cramér-von-Mises tests in the usual cases of real-valued random variables and random vectors with real components, and Gaigall (2019) for the application of a Cramér-von-Mises test for the null hypothesis of marginal homogeneity for bivariate distributions on the Cartesian square of the real line. However, the demand for consistency has a price: the distribution of the test statistic under the null hypothesis is unknown, and so related quantiles are not available in practice.…”

Section: Introductionmentioning

confidence: 99%

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Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

Ditzhaus

Gaigall

2022

TEST

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This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.

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Section: Testing Marginal Homogeneity In Hilbert Spacesmentioning

confidence: 99%

Section: Asymptotic Theory Of the Test Statisticmentioning

confidence: 99%

Section: Applications To Stock Market Returnsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

Ditzhaus

Gaigall

2022

TEST

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Homogeneity of marginal distributions for a large number of populations

Alba‐Fernández,

Jiménez‐Gamero

2023

Stat

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SummaryAssume that a random vector is observed in populations and independent samples of that random vector are available at each population. Assume that and have the same dimension. Our purpose is to test the equality of the marginal distributions of and in the populations when is large compared to the sample sizes. With this aim, we propose and study a test statistic that compares the empirical characteristic functions of the marginal distributions. Under the null, the test statistic is asymptotically free‐distributed. An expression of the asymptotic power is also derived, which allows to study the consistency of the test. No assumption is made on the distribution of and , which can be continuous, discrete or mixed; moreover, no assumption is made about moments. A simulation study investigates the finite sample performance of the new test. The proposal is applied to study air pollution levels that are directly related to environmental health, in all countries where observations are available.

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Hypothesis Testing for Matched Pairs with Missing Data by Maximum Mean Discrepancy: An Application to Continuous Glucose Monitoring

Matabuena

Félix

Ditzhaus

et al. 2023

The American Statistician

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Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data

Cited by 5 publications

References 40 publications

Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

Homogeneity of marginal distributions for a large number of populations

Hypothesis Testing for Matched Pairs with Missing Data by Maximum Mean Discrepancy: An Application to Continuous Glucose Monitoring

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