View source: R/fit_TylerCauchy.R
fit_Tyler  R Documentation 
Estimate parameters of a multivariate elliptical distribution, namely, the mean vector and the covariance matrix, to fit data. Any data sample with NAs will be simply dropped. The algorithm is based on Tyler's method, which normalizes the centered samples to get rid of the shape of the distribution tail. The data is first demeaned (with the geometric mean by default) and normalized. Then the estimation is based on the maximum likelihood estimation (MLE) and the algorithm is obtained from the majorizationminimization (MM) optimization framework. Since Tyler's method can only estimate the covariance matrix up to a scaling factor, a very effective method is employed to recover the scaling factor.
fit_Tyler(
X,
initial = NULL,
estimate_mu = TRUE,
max_iter = 200,
ptol = 0.001,
ftol = Inf,
return_iterates = FALSE,
verbose = FALSE
)
X 
Data matrix containing the multivariate time series (each column is one time series). 
initial 
List of initial values of the parameters for the iterative estimation method. Possible elements include:

estimate_mu 
Boolean indicating whether to estimate 
max_iter 
Integer indicating the maximum number of iterations for the iterative estimation
method (default is 
ptol 
Positive number indicating the relative tolerance for the change of the variables
to determine convergence of the iterative method (default is 
ftol 
Positive number indicating the relative tolerance for the change of the loglikelihood
value to determine convergence of the iterative method (default is 
return_iterates 
Logical value indicating whether to record the values of the parameters (and possibly the
loglikelihood if 
verbose 
Logical value indicating whether to allow the function to print messages (default is 
A list containing possibly the following elements:
mu 
Mean vector estimate. 
scatter 
Scatter matrix estimate. 
nu 
Degrees of freedom estimate (assuming an underlying Student's t distribution). 
cov 
Covariance matrix estimate. 
converged 
Boolean denoting whether the algorithm has converged ( 
num_iterations 
Number of iterations executed. 
cpu_time 
Elapsed CPU time. 
log_likelihood 
Value of loglikelihood after converge of the estimation algorithm (if 
iterates_record 
Iterates of the parameters ( 
Daniel P. Palomar
Ying Sun, Prabhu Babu, and Daniel P. Palomar, "Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms," IEEE Trans. on Signal Processing, vol. 62, no. 19, pp. 51435156, Oct. 2014.
fit_Cauchy
and fit_mvt
library(mvtnorm) # to generate heavytailed data
library(fitHeavyTail)
X < rmvt(n = 1000, df = 6) # generate Student's t data
fit_Tyler(X)
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