testKron_A: Testing Kronecker product structure along specified modes

In KOFM: Test the Kronecker Product Structure in Tensor Factor Models

Testing Kronecker product structure along specified modes

Description

Testing the Kronecker product structure of a tensor time series with a specified set of mode indices.

Usage

testKron_A(ten, AA, r, alpha = c(0.01, 0.05), q = 0.05, r.exact = FALSE)

Arguments

ten	An array representing an order-(K+1) tensor which is an order-K tensor time series with mode-1 being the time mode.
AA	A vector with elements at least 1 and at most K, representing the tensor modes to test.
r	A vector representing the rank for 'ten'.
alpha	A vector representing the desired significance levels. Default is c(0.01, 0.05).
q	A number between 0 and 1, representing the quantile for the decision statistic. Default is 0.05.
r.exact	Logical. Perform the test only using 'r' if TRUE, otherwise using all divisor combinations of the last mode rank of the reshaped data. Default is FALSE.

Value

A list containing the following: level: a matrix with each entry reporting an example test size, corresponding to its rank used (row) and level of alpha (column); the alpha is reported in order of parameter 'alpha'. decision: a matrix with each entry reporting the decision statistic aggregated by quantile of parameter 'q', corresponding to its rank used (row) and level of alpha (column); the alpha is reported in order of parameter 'alpha'. rank: a matrix with K columns and each row represents a different rank used, corresponding to the rows in the 'level' and 'decision' matrices.

KOFM documentation built on April 3, 2025, 11:05 p.m.