This function is to estimate row and column sample matrix Kendall's tau which are defined in He et al. (2022) &lt;arXiv:2207.09633&gt;

Large-scale matrix-variate data have been widely observed nowadays in various research areas such as finance, signal processing and medical imaging. Modelling matrix-valued data by matrix-elliptical family not only provides a flexible way to handle heavy-tail property and tail dependencies, but also maintains the intrinsic row and column structure of random matrices. We proposed a new tool named matrix Kendall's tau which is efficient for analyzing random elliptical matrices. By applying this new type of Kendell’s tau to the matrix elliptical factor model, we propose a Matrix-type Robust Two-Step (MRTS) method to estimate the loading and factor spaces. See the details in He at al. (2022) <arXiv:2207.09633>. In this package, we provide the algorithms for calculating sample matrix Kendall's tau, the MRTS method and the Matrix Kendall's tau Eigenvalue-Ratio (MKER) method which is used for determining the number of factors.

Yalin Wang

MKendall

Matrix Kendall's Tau and Matrix Elliptical Factor Model

Yong He

Long Yu

Wang Zhou

Wenxin Zhou

MSK function

<dl> <dt>X</dt>
<dd>Input three-dimensional array, of dimension \(T \times p \times q\).
\(T\) is the sample size, \(p\) is the row dimension of each matrix observation and \(q\) is the column dimension of each matrix observation.</dd> <dt>type</dt>
<dd>If type=1, calculate the row sample matrix Kendall's tau; if type=2, calculate the column sample matrix Kendall's tau. The default is the row sample matrix Kendall's tau.</dd></dl>

Arguments

Yong He, Yalin Wang, Long Yu, Wang Zhou and Wenxin Zhou.

Author

Estimating Row and Column Sample Matrix Kendall's Tau — MSK

<dl>

 <dt>X</dt>
<dd>Input three-dimensional array, of dimension \(T \times p \times q\).
\(T\) is the sample size, \(p\) is the row dimension of each matrix observation and \(q\) is the column dimension of each matrix observation.</dd>

 <dt>type</dt>
<dd>If type=1, calculate the row sample matrix Kendall's tau; if type=2, calculate the column sample matrix Kendall's tau. The default is the row sample matrix Kendall's tau.</dd>

</dl>

MSK: Estimating Row and Column Sample Matrix Kendall's Tau

Description

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Examples