PMLE.SEF3.free {double.truncation}

Parametric Inference for the three-parameter SEF model (free parameter space for eta_3)

Description

Maximum likelihood estimates and their standard errors (SEs) are computed. Also computed are the likelihood value, AIC, and other qnantities.

Usage

PMLE.SEF3.free(u.trunc, y.trunc, v.trunc,
 tau1 = min(y.trunc), tau2 = max(y.trunc),
 epsilon = 1e-04, D1=20, D2=10, D3=1, d1=6, d2=0.5)

Arguments

u.trunc

lower truncation limit

y.trunc

variable of interest

v.trunc

upper truncation limit

tau1

lower support

tau2

upper support

epsilon

error tolerance for Newton-Raphson

D1

Divergence condition for eta_1

D2

Divergence condition of eta_2

D3

Divergence condition of eta_3

d1

Range of randomization for eta_1

d2

Range of randomization for eta_2

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

## The first 10 samples of the childhood cancer data ##
y.trunc=c(6,7,15,43,85,92,96,104,108,123)
u.trunc=c(-1643,-24,-532,-1508,-691,-1235,-786,-261,-108,-120)
v.trunc=u.trunc+1825
PMLE.SEF3.free(u.trunc,y.trunc,v.trunc)