HPCA_FN {HDRFA}

Estimating Factor Numbers via Rank Minimization Corresponding to Huber PCA

Description

This function is to estimate factor numbers via rank minimization corresponding to Huber Principal Component Analysis (HPCA).

Usage

HPCA_FN(X, rmax, Method = "E", tau = NULL, scale_est="MAD", threshold = NULL,
        L_init = NULL, F_init = NULL, maxiter_HPCA = 100, maxiter_HLM = 100, 
        eps = 0.001)

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.

Method

Method="P" indicates minimizing the Huber loss of the idiosyncratic error's \ell_2 norm while Method="E" indicates minimizing the elementwise Huber loss. The default is the elementwise Huber loss.

tau

Optional user-supplied parameter for Huber loss; default is NULL, and \tau is provided by default.

scale_est

A parameter for the elementwise Huber loss. scale_est="MAD" indicates robust variance estimation in each iteration, while scale_est="const" indicates fixing user-supplied \tau. The default is scale_est="MAD".

threshold

The threshold of rank minimization; default is NULL.

L_init

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

F_init

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

maxiter_HPCA

The maximum number of iterations in the HPCA. The default is 100.

maxiter_HLM

The maximum number of iterations in the iterative Huber regression algorithm. The default is 100.

eps

The stopping critetion parameter in the HPCA. The default is 1e-3.

Details

See He et al. (2023) for details.

Value

rhat

The estimated factor number.

Author(s)

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

References

He Y, Li L, Liu D, Zhou W., 2023 Huber Principal Component Analysis for Large-dimensional Factor Models.

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


HPCA_FN(X,8,Method="E")

HPCA_FN(X,8,Method="P")