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Related Concept Videos

Hypothesis Test for Test of Independence01:16

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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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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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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...
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Extending Hilbert-Schmidt Independence Criterion for Testing Conditional Independence.

Bingyuan Zhang1, Joe Suzuki1

  • 1Graduate School of Engineer Science, Osaka University, Toyonaka 560-0043, Japan.

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|March 29, 2023
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Summary

This study introduces a new nonparametric Conditional Independence (CI) test using kernel methods and local bootstrap. The novel approach significantly improves performance, especially with high-dimensional data.

Keywords:
conditional independence testdependence measurelocal bootstrap

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Conditional Independence (CI) testing is crucial in statistical inference.
  • Existing nonparametric CI tests struggle with high-dimensional conditioning sets.
  • Kernel-based methods offer potential for improved CI testing.

Purpose of the Study:

  • To develop a robust nonparametric CI test effective for high-dimensional conditioning sets.
  • To extend the Hilbert-Schmidt Independence Criterion (HSIC) for enhanced CI testing.
  • To introduce a local bootstrap method for accurate null distribution sampling.

Main Methods:

  • Kernel-based test statistic, an extension of HSIC.
  • Local bootstrap for generating samples under the null hypothesis (X⫫Y∣Z).
  • Evaluation against existing nonparametric CI tests.

Main Results:

  • Significant performance improvement over previous methods.
  • Sustained effectiveness with increasing dimension of the conditioning set.
  • Efficient computation with growing sample size and conditioning set dimension.

Conclusions:

  • The proposed kernel-based CI test with local bootstrap is a powerful advancement.
  • This method overcomes limitations of existing tests in high-dimensional scenarios.
  • The approach offers computational efficiency and robust performance.