estimateM | R Documentation |
estimate.Mxxx computes the maximum likelihood estimates for the distribution xxx, where xxx is any supported model in the multivariate scale mixtures of normal (MSMN), multivariate scale mixtures of skew-normal (MSMSN), multivariate skew scale mixtures of normal (MSSMN) or multivariate scale mixtures of skew-normal-Cauchy (MSMSNC) classes. See details for supported distributions.
estimate.MN(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE)
estimate.MT(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.min = 2.0001)
estimate.MSL(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.min = 2.0001)
estimate.MCN(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE)
estimate.MSN(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE)
estimate.MSTN(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.min = 2.0001)
estimate.MSSL(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.min = 2.0001)
estimate.MSCN(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE)
estimate.MSTT(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 3, nu.min = 2.0001)
estimate.MSSL2(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 3, nu.min = 2.0001)
estimate.MSCN2(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 0.5, gamma.fixed = 0.5)
estimate.MSNC(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE)
estimate.MSTEC(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 3, nu.min = 2.0001)
estimate.MSSLEC(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 3, nu.min = 2.0001)
estimate.MSCEC(y, X, max.iter = 1000, prec = 1e-04, est.var = TRUE,
nu.fixed = 0.5, gamma.fixed = 0.5)
y |
The multivariate vector of responses. The univariate case also is supported. |
X |
The regressor matrix. |
max.iter |
The maximum number of iterations. |
prec |
The convergence tolerance for parameters. |
est.var |
Logical. If TRUE the standard errors are estimated. |
nu.fixed |
If a numerical value is provided, the estimation consider nu as fixed. To estimate nu, use nu.fixed=FALSE. Avaliable for MSTT, MSSL2, MSCN2, MSTEC, MSSLEC and MSCEC distributions. For MSTT, MSSL2, MSTEC and MSSLEC, the default value is 3 and nu should be greater than 1. For MSCN2 and MSCEC, the default value is 0.5 and nu should be in the (0,1) interval. |
gamma.fixed |
If a numerical value is provided, the estimation consider gamma as fixed. To estimate gamma, use gamma.fixed=FALSE. Avaliable for MSCN2 and MSCEC distributions. For MSCN2 and MSCEC, the default value is 0.5 and gamma should be in the (0,1) interval. |
nu.min |
Lower value to perform the maximization for nu. For MSTT, MSSL2, MSTEC and MSSLEC is used only when nu.fixed=FALSE. |
Supported models are:
In MSMN class: multivariate normal (MN), multivariate Student t (MT), multivariate slash (MSL), multivariate contaminated normal (MCN). See Lange and Sinsheimer (1993) for details.
In MSMSN class: multivariate skew-normal (MSN), multivariate skew-T (MSTT), multivariate skew-slash (MSSL2), multivariate skew-contaminated normal (MSCN2). See Zeller, Lachos and Vilca-Labra (2011) for details.
In MSSMN class: MSN, multivariate skew-t-normal (MSTN), multivariate skew-slash normal (MSSL), multivariate skew-contaminated normal (MSCN). See Louredo, Zeller and Ferreira (2021) for details.
In MSMSNC class: multivariate skew-normal-Cauchy (MSNC), multivariate skew-t-Expected-Cauchy (MSTEC), multivariate skew-slash-Expected-Cauchy (MSSLEC), multivariate skew-contaminated-Expected-Cauchy (MSCEC). See Kahrari et al. (2020) for details.
Note: the MSN distribution belongs to both, MSMSN and MSSMN classes.
an object of class "skewMLRM" is returned. The object returned for this functions is a list containing the following components:
coefficients |
A named vector of coefficients |
se |
A named vector of the standard errors for the estimated coefficients. Valid if est.var is TRUE and the hessian matrix is invertible. |
nu |
The estimated or fixed nu (only for MSTT, MSSL2, MSCN2, MSTEC, MSSLEC and MSCEC models) |
gamma |
The estimated or fixed gamma (only for MSCN2 and MSCEC models) |
logLik |
The log-likelihood function evaluated in the estimated parameters |
AIC |
Akaike's Information Criterion |
BIC |
Bayesian's Information Criterion |
iterations |
the number of iterations until convergence (if attached) |
time |
execution time in seconds |
conv |
An integer code. 0 indicates successful completion. 1 otherwise. |
dist |
The distribution for which was performed the estimation. |
class |
The class for which was performed the estimation. |
n |
The sample size |
y |
The multivariate vector of responses. The univariate case also is supported. |
X |
The regressor matrix (in a list form). |
function |
a string with the name of the used function. |
In MT, MSL, MSTN, MSSL, MSTT, MSSL2, MSTEC and MSSLEC distributions, nu>2 guarantees that the mean and variance exist, nu>1 guarantees the existence only for the mean and for nu<=1, the mean and variance of the distribution is not finite.
Clecio Ferreira, Diego Gallardo and Camila Zeller
Kahrari, F., Arellano-Valle, R.B., Ferreira, C.S., Gallardo, D.I. (2020) Some Simulation/computation in multivariate linear models of scale mixtures of skew-normal-Cauchy distributions. Communications in Statistics - Simulation and Computation. In press. DOI: 10.1080/03610918.2020.1804582
Lange, K., Sinsheimer, J.S. (1993). Normal/independent distributions and their applications in robust regression. Journal of Computational and Graphical Statistics 2, 175-198.
Louredo, G.M.S., Zeller, C.B., Ferreira, C.S. (2021). Estimation and influence diagnostics for the multivariate linear regression models with skew scale mixtures of normal distributions. Sankhya B. In press. DOI: 10.1007/s13571-021-00257-y
Zeller, C.B., Lachos, V.H., Vilca-Labra, F.E. (2011). Local influence analysis for regression models with scale mixtures of skew-normal distributions. Journal of Applied Statistics 38, 343-368.
data(ais, package="sn") ##Australian Institute of Sport data set
attach(ais)
##It is considered a bivariate regression model
##with Hg and SSF as response variables and
##Hc, Fe, Bfat and LBM as covariates
y<-cbind(Hg,SSF)
n<-nrow(y); m<-ncol(y)
X.aux=model.matrix(~Hc+Fe+Bfat+LBM)
p<-ncol(X.aux)
X<-array(0,dim=c(2*p,m,n))
for(i in 1:n) {
X[1:p,1,i]=X.aux[i,,drop=FALSE]
X[p+1:p,2,i]=X.aux[i,,drop=FALSE]
}
##See the covariate matrix X
##X
fit.MN=estimate.MN(y, X) ##Estimate the parameters for the MN regression model
summary(fit.MN)
fit.MT=estimate.MT(y, X) ##Estimate the parameters for the MT regression model
summary(fit.MT)
##may take some time on some systems
fit.MSSL=estimate.MSSL(y, X) ##Estimate the parameters for the MSSL regression model
summary(fit.MSSL)
fit.MSTT=estimate.MSTT(y, X) ##Estimate the parameters for the MSTT regression model
summary(fit.MSTT)
fit.MSNC=estimate.MSNC(y, X) ##Estimate the parameters for the MSNC regression model
summary(fit.MSNC)
fit.MSCEC=estimate.MSCEC(y, X) ##Estimate the parameters for the MSCEC regression model
summary(fit.MSCEC)
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