HPCA_FN: Estimating Factor Numbers via Rank Minimization Corresponding...

In HDRFA: High-Dimensional Robust Factor Analysis

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")

HDRFA documentation built on Sept. 11, 2024, 9:25 p.m.