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A characterization of multivariate normality through univariate projections
1Division of Biostatistics, New York University SOM, 650 First Avenue, New York, NY 10016, USA ; Department of Statistics, Iowa State University, Ames, IA 50011, USA.
Journal of Multivariate Analysis
|November 26, 2013
Summary
This study presents a novel method for characterizing multivariate normality. It proves that a random vector is multivariate normal if and only if all its linear combinations are univariate normal.
Area of Science:
- Statistics
- Probability Theory
Background:
- Multivariate normality is a fundamental concept in statistics.
- Existing characterizations often involve complex conditions or specific distributions.
Purpose of the Study:
- To introduce a new, simpler characterization of multivariate normality.
- To establish a condition based on the normality of linear combinations of a random vector's components.
Main Methods:
- The study utilizes linear algebra and probability theory.
- It analyzes the properties of linear transformations of random vectors.
Main Results:
- A new theorem is presented: a random vector possesses multivariate normality if and only if every linear combination of its components exhibits univariate normality.
- This provides a practical criterion for assessing multivariate normality.
Conclusions:
- The proposed characterization offers an alternative and potentially more accessible approach to verifying multivariate normality.
- This finding has implications for statistical inference and modeling where multivariate normality is assumed.
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