Help for package REFA

Type:

Package

Title:

Robust Exponential Factor Analysis

Date:

2023-11-01

Version:

0.1.0

Author:

Jiaqi Hu [cre, aut], Xueqin Wang [aut]

Maintainer:

Jiaqi Hu <hujiaqi@mail.ustc.edu.cn>

Description:

A robust alternative to the traditional principal component estimator is proposed within the framework of factor models, known as Robust Exponential Factor Analysis, specifically designed for the modeling of high-dimensional datasets with heavy-tailed distributions. The algorithm estimates the latent factors and the loading by minimizing the exponential squared loss function. To determine the appropriate number of factors, we propose a modified rank minimization technique, which has been shown to significantly enhance finite-sample performance.

Imports:

mvtnorm

Depends:

R (≥ 3.5.0)

License:

GPL-3

Encoding:

UTF-8

RoxygenNote:

7.2.3

NeedsCompilation:

Packaged:

2023-11-18 03:28:45 UTC; hujiaqi

Repository:

CRAN

Date/Publication:

2023-11-19 15:20:05 UTC

Estimation of errors for common component

Description

Estimation of errors for common component

Usage

ECC(Chat, C)

Arguments

Chat

The estimated common component

C

The true common component

Value

a numeric value of the ECC

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples


dat = gendata()
Y = dat$Y
F0 = dat$F0
L0 = dat$L0
C0 = F0 
res = REFA(dat$Y, r = 3)
Fhat = res$Fhat
Lhat = res$Lhat
Chat = Fhat 
ECC(Chat, C0)

Principal Component Analysis for Factor Models

Description

Principal Component Analysis for Factor Models

Usage

FA(X, r)

Arguments

X

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

r

A positive integer indicating the factor numbers.

Value

Fhat

The estimated factor matrix.

Lhat

The estimated loading matrix.

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples

##---- Should be DIRECTLY executable !! ----

Robust Exponential Factor Analysis

Description

Robust Exponential Factor Analysis

Usage

REFA(Y, r = 3, tau = 0.75, q = 0.05, eps = 1e-05, init = TRUE)

Arguments

Y

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

r

A positive integer indicating the factor numbers.

q

Hyper parameter

eps

The stopping criterion parameter. The default is 1e-5.

tau

Hyper parameter

init

Warn start of the algorithm. If init = TRUE, use modified PCA initialization. If init is a list contains F0 and L0, we will use this initialization. Otherwise, use traditional PCA initialization.

Value

Fhat

The estimated factor matrix.

Lhat

The estimated loading matrix.

loss

the value of the loss function.

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples


dat = gendata()
REFA(dat$Y, r = 3)

Estimating Factor Numbers via Modified Rank Minimization

Description

Estimating Factor Numbers via Modified Rank Minimization

Usage

REFA_FN(Y, rmax = 8, tau = 0.75, q = 0.1, eps = 1e-04, init = TRUE)

Arguments

Y

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

rmax

The bound of the number of factors.

q

Hyper parameter in modified PCA algorithm. Default is 0.05.

eps

The stopping criterion parameter. Default is 1e-5.

tau

Hyper parameter in selecting \gamma of the loss function.

init

Warn start by modified PCA algorithm. Default is TRUE.

Value

rhat

The estimated factor number.

Fhat

The estimated factor matrix.

Lhat

The estimated loading matrix.

loss

the value of the loss function.

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples


dat = gendata()
REFA_FN(dat$Y, rmax = 8)

Trace ratios

Description

Trace ratios

Usage

TR(Fhat, F0)

Arguments

Fhat

The estimated factors.

F0

The true factors.

Value

a numeric value of the trace ratios.

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples


dat = gendata()
Y = dat$Y
F0 = dat$F0
res = REFA(dat$Y, r = 3)
Fhat = res$Fhat
TR(Fhat, F0)

Estimating Factor Numbers Corresponding PCA

Description

Estimating Factor Numbers Corresponding PCA

Usage

est_num(X, kmax = 8, type = "BIC3")

Arguments

X

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

kmax

The user-supplied maximum factor numbers.

type

the method used.

Value

the estimated factor numbers

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples


dat = gendata()
est_num(dat$Y)

Data generation process

Description

Generate heavy-tailed data.

Usage

gendata(seed = 1, T = 50, N = 50, type = "1a")

Arguments

seed

the seed used in the data generation process.

T

time dimension.

N

cross-sectional dimension.

type

the type of the data generation process, it can be "1a", "1b", "1c", "1d", "2a", "2b", "2c", "2d".

Value

a list consisting of Y, F0, L0.

Author(s)

Jiaqi Hu

References

Manuscript: Robust factor analysis with exponential squared loss

Examples

dat = gendata()
Y = dat$Y
head(Y)