PMLE.SEF2.negative {double.truncation} | R Documentation |
Parametric Inference for the two-parameter SEF model (negative parameter space for eta_2)
Description
Maximum likelihood estimates and their standard errors (SEs) are computed. Also computed are the likelihood value, AIC, and other qnantities. Since this is the model, estimates for the mean and SD are also computed.
Usage
PMLE.SEF2.negative(u.trunc, y.trunc, v.trunc, epsilon = 1e-04)
Arguments
u.trunc |
lower truncation limit |
y.trunc |
variable of interest |
v.trunc |
upper truncation limit |
epsilon |
error tolerance for Newton-Raphson |
Details
Details are seen from the references.
Value
eta |
estimates |
SE |
standard errors |
convergence |
Log-likelihood, degree of freedom, AIC, the number of iterations |
Score |
score vector at the converged value |
Hessian |
Hessian matrix at the converged value |
Author(s)
Takeshi Emura, Ya-Hsuan Hu
References
Hu YH, Emura T (2015) Maximum likelihood estimation for a special exponential family under random double-truncation, Computation Stat 30 (4): 1199-229
Emura T, Hu YH, Konno Y (2017) Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation, Stat Pap 58 (3): 877-909
Dorre A, Emura T (2019) Analysis of Doubly Truncated Data, An Introduction, JSS Research Series in Statistics, Springer
Examples
### Data generation: see Appendix of Hu and Emura (2015)
n=300
eta1_true=30
eta2_true=-0.5
mu_true=30
mu_u=29.09
mu_v=30.91
a=u=v=y=c()
###generate n samples of (ui,yi,vi) subject to ui<=yi<=vi###
j=1
repeat{
u[j]=rnorm(1,mu_u,1)
v[j]=rnorm(1,mu_v,1)
y[j]=rnorm(1,mu_true,1)
if(u[j]<=y[j]&&y[j]<=v[j]) a[j]=1 else a[j]=0
if(sum(a)==n) break ###we need n data set###
j=j+1
}
mean(a) ### inclusion probability around 0.5 ###
v.trunc=v[a==1]
y.trunc=y[a==1]
u.trunc=u[a==1]
PMLE.SEF2.negative(u.trunc,y.trunc,v.trunc)