Testing heteroskedasticity in trace regression with low-rank matrix parameter

Heteroskedasticity testing is crucial in regression analysis, yet research on heteroskedasticity tests for matrix data remains limited. This article introduces a novel approach for testing heteroskedasticity in trace regression, using the nuclear norm penalty to account for the low-rank structure of the unknown parameters. Under some mild conditions and the null hypothesis, we derive the asymptotic distribution of the test statistic. Both simulation results and analyses of real data demonstrate that the proposed testing procedure performs well.