Fit univariate NL-SMSN regression

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Description

Return EM algorithm output for NL-SMSN regression for both "Homoscedastic" and "Heteroscedastic" (univaritate case, p=1).

Usage

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smsn.nl(y, x = NULL, z = NULL, betas = NULL, sigma2 = NULL, shape = NULL, rho = NULL, 
        nu = NULL, nlf = NULL, rho.func = 1, reg.type = "Homoscedastic", criteria = FALSE, 
        family = "Skew.t", error = 1e-05, iter.max = 100)

Arguments

y

the response vector

x

the independent covariates

z

the independent covariates for sigma2. "Heteroscedastic" model ONLY!

betas

regression coefficient(s) vector

sigma2

initial value for the scale parameter

shape

initial value for the skewness parameter

rho

initial value for "Heteroscedastic" coefficient rho. "Heteroscedastic" model ONLY!

nu

the parameter of the scale variable (vector or scalar) of the SMSN family (kurtosis parameter). For the "Skew.cn" must be a vector of length 2 and values in (0,1)

nlf

non linear function for the regression

rho.func

Choose the type of heteroscedasticity for sigma2. If rho.func == 1 ( f(z,rho) = exp(z*rho) ) and rho.func == 2 ( f(z,rho) = z^rho ).

reg.type

the type of possible regression: "Homoscedastic" or "Ho"; "Heteroscedastic" or "He".

criteria

if TRUE, loglik, AIC, BIC will be calculated

family

distribution famility to be used in fitting ("t", "Skew.t", "Skew.cn", "Skew.slash", "Skew.normal", "Normal")

error

the covergence maximum error

iter.max

maximum iterations of the EM algorithm

Value

Estimated values of the location, scale, skewness, regression coefficients and "Heteroscedastic" coefficient (when reg.type = "He").

Author(s)

Aldo Garay amedina@ime.usp.br, Marcos Prates marcosop@est.ufmg.br and Victor Lachos hlachos@ime.unicamp.br

References

Aldo M. Garay, Victor H. Lachos, Carlos A. Abanto-Valle (2011). "Nonlinear regression models based on scale mixture of skew-normal distributions". Journal of the Korean Stastical Society, 40, 115-124.\

Victor H. Lachos, Dipankar Bandyopadhyay and Aldo M. Garay (2011). "Heteroscedastic nonlinear regression models based on scale mixture of skew-normal distributions". Statistics -and Probability Letters, 81, 1208-1217.

Examples

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 ##see examples in \code{\link{Oil}} and \code{\link{Ultrasonic}} 

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