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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

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:
H0: The two variables (factors)...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

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.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

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Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models.

Jianqing Fan1, Yang Feng, Rui Song

  • 1Jianqing Fan is Frederick L. Moore Professor of Finance, Department of Operations Research and Financial Engineering, Princeton University, Princeton NJ 08544 ( jq-fan@princeton.edu ). Yang Feng is Assistant Professor, Department of Statistics, Columbia University, New York, NY 10027 ( yangfeng@stat.columbia.edu ). Rui Song is Assistant Professor, Department of Statistics, Colorado State University, Fort Collins, CO 80523 ( song@stat.colostate.edu ).

Journal of the American Statistical Association
|January 27, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces Nonparametric Independence Screening (NIS) to improve variable selection in high-dimensional data, especially when relationships are nonlinear. The new method, NIS, effectively screens relevant variables for better model fitting.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • High-dimensional models present challenges in variable selection.
  • Existing correlation learning methods may fail with nonlinear marginal regression.
  • Sparse ultra-high dimensional models require efficient dimensionality reduction techniques.

Purpose of the Study:

  • To extend correlation learning to nonparametric settings for variable screening.
  • To introduce Nonparametric Independence Screening (NIS) as a sure independence screening method.
  • To develop enhanced procedures for sparse additive models.

Main Methods:

  • Extension of correlation learning to marginal nonparametric learning.
  • Development of Nonparametric Independence Screening (NIS).
  • Proposal of data-driven thresholding and Iterative Nonparametric Independence Screening (INIS).

Main Results:

  • The proposed NIS methods achieve a sure screening property under general nonparametric models.
  • Quantification of dimensionality reduction achievable by independence screening.
  • Demonstrated effectiveness of NIS and INIS in simulations and real data analysis.

Conclusions:

  • Nonparametric Independence Screening (NIS) offers a robust approach for variable selection in high-dimensional data.
  • The proposed methods enhance performance for sparse additive models.
  • NIS and INIS outperform competing methods, especially with moderate sample sizes and large dimensions.