PMLE.SEF1.free: Parametric inference for the one-parameter SEF model (free...

In double.truncation: Analysis of Doubly-Truncated Data

Description

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

Usage

PMLE.SEF1.free(u.trunc, y.trunc, v.trunc,
 tau1 = min(y.trunc), tau2 = max(y.trunc), epsilon = 1e-04)

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

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 at the converged value
Hessian	Hessian at the converged value

Author(s)

Takeshi Emura

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) ###
eta_true=-3
eta_u=-9
eta_v=-1
tau=10
n=300

a=u=v=y=c()

j=1
repeat{
  u1=runif(1,0,1)
  u[j]=tau+(1/eta_u)*log(1-u1)
  u2=runif(1,0,1)
  v[j]=tau+(1/eta_v)*log(1-u2)
  u3=runif(1,0,1)
  y[j]=tau+(1/eta_true)*log(1-u3)
  if(u[j]<=y[j]&&y[j]<=v[j]) a[j]=1 else a[j]=0
  if(sum(a)==n) break
  j=j+1
}
mean(a) ## inclusion probability around 0.5
  
v.trunc=v[a==1]
u.trunc=u[a==1]
y.trunc=y[a==1]

PMLE.SEF1.free(u.trunc,y.trunc,v.trunc)

double.truncation documentation built on Sept. 8, 2020, 9:07 a.m.