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Related Concept Videos

Test for Homogeneity01:23

Test for Homogeneity

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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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Homogeneity tests for one-way models with dependent errors under correlated groups.

Yuichi Goto1, Koichi Arakaki2, Yan Liu3,4

  • 1Department of Mathematical Sciences, Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395 Japan.

Test (Madrid, Spain)
|September 12, 2022
PubMed
Summary
This summary is machine-generated.

A new asymptotically distribution-free test statistic is proposed for one-way models with correlated groups and dependent disturbances. This novel approach overcomes limitations of the classical F-statistic, offering robust detection of fixed and random effects.

Keywords:
Dynamic panel dataFixed effectHomogeneity testLongitudinal dataOne-way modelRandom effect

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Area of Science:

  • Econometrics
  • Statistical Inference
  • Time Series Analysis

Background:

  • Classical F-statistic in analysis of variance is not suitable for one-way models with correlated groups and dependent disturbances.
  • Existing methods lack asymptotic distribution-freeness under these complex dependency structures.
  • Accurate testing for fixed and random effects is crucial in various fields, including finance and econometrics.

Purpose of the Study:

  • To develop a new, asymptotically distribution-free test statistic for detecting fixed and random effects in one-way models.
  • To address the limitations of the classical F-statistic in settings with correlated groups and dependent disturbances.
  • To provide a robust statistical tool applicable to financial data and other complex models.

Main Methods:

  • Proposed a novel test statistic that extends the classical F-statistic while being asymptotically distribution-free.
  • Developed theoretical guarantees for the new test, including asymptotic size and consistency.
  • Investigated the power of the test under local alternatives.
  • Validated theoretical findings through extensive numerical simulations using various disturbance models (time series, GARCH, heavy-tailed, skewed).

Main Results:

  • The proposed test statistic is asymptotically distribution-free, irrespective of underlying disturbance distributions.
  • The new tests demonstrate asymptotic size control and consistency.
  • The test exhibits nontrivial power under local alternatives, indicating sensitivity to subtle effects.
  • Numerical simulations confirm the theoretical results across diverse and complex disturbance models.
  • Application to stock log-returns successfully uncovered significant random effects in specific sectors.

Conclusions:

  • The developed test statistic offers a robust and reliable method for testing fixed and random effects in challenging one-way models.
  • The asymptotically distribution-free nature of the test makes it broadly applicable without stringent distributional assumptions.
  • The successful application to financial data highlights its practical utility in uncovering hidden effects in real-world datasets.