PMLE.Normal: Parametric Inference for Bivariate Normal Models with...

In depend.truncation: Statistical Methods for the Analysis of Dependently Truncated Data

Description

Maximum likelihood estimation (MLE) for dependent truncation data under the bivariate normal distribution. A bivariate normal distribution is assumed for bivariate random variables (L, X). The truncated data (L_j, X_j), subject to L_j<=X_j for all j=1, ..., n, are used to obtain the MLE for the population parameters of (L, X).

Usage

PMLE.Normal(l.trunc, x.trunc, testimator = FALSE,GOF=TRUE)

Arguments

l.trunc	vector of truncation variables satisfying l.trunc<=x.trunc
x.trunc	vector of variables satisfying l.trunc<=x.trunc
testimator	if TRUE, testimator is computed instead of MLE
GOF	if TRUE, goodness-of-fit test is performed

Details

PMLE.Normal performs the maximum likelihood estimation for dependently left-truncated data under the bivariate normal distribution. "PMLE.Normal" implements the methodologies developed in Emura T. & Konno Y. (2012, Statistical Papers 53, 133-149)and can produce the maximum likelihood estimates and their standard errors. Furthermore, "PMLE.Normal" tests the independence assumption between truncation variable and variable of interest via likelihood ratio test. The MLE is obtained by minimizing -logL using "nlm", where L is the log-likelihood.

Value

mu_L	mean of L and its standard error
mu_X	mean of X and its standard error
var_L	variance of L and its standard error
var_X	variance of X and its standard error
cov_LX	covariance between L and X and its standard error
c	inclusion probability, defined by c=Pr(L<=X), and its standard error
test	Likelihood ratio statistic and p-value
C	Cramer-von Mises goodness-of-fit test statistics
K	Kolmogorov-Smirnov goodness-of-fit test statistics

Author(s)

Takeshi EMURA

References

Emura T, Konno Y (2012), Multivariate Normal Distribution Approaches for Dependently Truncated Data. Statistical Papers 53 (No.1), 133-149.

Emura T, Konno Y (2014), Erratum to: Multivariate Normal Distribution Approaches for Dependently Truncated Data, Statistical Papers 55 (No.4): 1233-36

Examples

l.trunc=c(1,2,3,4,5,6,7,8,8)
x.trunc=c(2,4,4,5,5,7,7,9,10)
PMLE.Normal(l.trunc,x.trunc,testimator=FALSE)

depend.truncation documentation built on May 2, 2019, 3:04 a.m.