HDRFA (version 0.1.5)

IQR_FN: Estimating Factor Numbers via Rank Minimization Corresponding to IQR

Description

This function is to estimate factor numbers via rank minimization corresponding to Iterative Quantile Regression (IQR).

Usage

IQR_FN(X, rmax, tau, threshold = NULL, L_init = NULL, F_init = NULL, 
       max_iter = 100, eps = 10^(-6))

Value

rhat

The estimated factor number.

Arguments

X

Input matrix, of dimension \(T\times N\). Each row is an observation with \(N\) features at time point \(t\).

rmax

The user-supplied maximum factor numbers.

tau

The user-supplied quantile level.

threshold

The threshold of rank minimization; default is NULL.

L_init

User-supplied inital value of loadings in the IQR; default is the PCA estimator.

F_init

User-supplied inital value of factors in the IQR; default is the PCA estimator.

max_iter

The maximum number of iterations. The default is \(100\).

eps

The stopping critetion parameter of the IQR method. The default is 1e-06.

Author

Yong He, Lingxiao Li, Dong Liu, Wenxin Zhou.

Details

See Chen et al. (2021) for more details.

References

Chen, L., Dolado, J.J., Gonzalo, J., 2021. Quantile factor models. Econometrica 89, 875–910.

Examples

set.seed(1)
T=50;N=50;r=3
L=matrix(rnorm(N*r,0,1),N,r);F=matrix(rnorm(T*r,0,1),T,r)
E=matrix(rnorm(T*N,0,1),T,N)
X=F%*%t(L)+E

tau=0.5
IQR_FN(X,8,tau)