M3.gmm: Estimating the latent factors using third-order generalized...

In GuanglinHuang/hofa: higher-order multi-cumulant factor analysis

Estimating the latent factors using third-order generalized moment methods

Description

Estimating the latent factors and factor loadings in high dimensional factor model using generalized moment methods based on the third-order cumulant.

Usage

M3.gmm(
  X,
  r,
  kappa = 0,
  initial = c("PCA", "MLE"),
  W_diag = FALSE,
  identity = FALSE,
  delta = NULL,
  eps = 10^-6,
  ...
)

Arguments

X	A matrix or data frame with t rows (samples) and n columns (variables).
r	The number of factors.
kappa	An integer. The weight between M and VWV, M denotes the covariance matrix and VWV denotes the GMM matrix. kappa default to 0.
initial	The method used to initialize the factor loadings and the moments of error. PCA denotes Principal Component Analysis and MLE denotes Maximum Likelihood Estimation in Bai and Li(2012).
W_diag	Logical. If TRUE, the weight matrix W only has nonzero diagonal elements, default to FALSE.
identity	Logical. If TRUE, the moments of errors are unified to identity, default to FALSE.
delta	An integer. The hard threshold value of W matrix in order to guarantee non-singularity of W, default to 1/log(t).
eps	The iteration error, default to 10^-6. Available for initializing the estimators by Maximum Likelihood method.
...	Any other parameters.

Value

A list of factors, factor loadings and other information, see below.

• f Estimated factors.

• u Estimated factor loadings.

• e Estimated errors.

• ev Eigenvalues of covariance matrix.

Examples

n = 100
t = 200
k = 2
par_f = list(rep(1,k),rep(0.8,k),rep(1,k),rep(Inf,k))
par_e = list(1,0,2,Inf)
rho_f = c(0.5,0.2)
par_cove = list(beta = 0.2,J = n/10,rho = 0.2,msig_e = c(1,5))
data = hofa.DGP2(n,t,k,par_f,par_e,par_cove,rho_f)$X
M3.gmm(data,r = 2,kappa = 0,initial = "PCA")

GuanglinHuang/hofa documentation built on Sept. 3, 2023, 7:01 a.m.