PMLE.SEF1.free {double.truncation}

Parametric inference for the one-parameter SEF model (free parameter space)

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)