. Author manuscript; available in PMC: 2016 Mar 7.

Published in final edited form as: Lifetime Data Anal. 2011 Nov 18;18(1):58–79. doi: 10.1007/s10985-011-9210-4

Table 1.

Simulation means for various estimators of the cumulative type 1 failure hazards at time 4.32 in the continuous setting with a sample size n = 100 under misattribution, logit r(t) = (logit ψ₀) + ψ₁t. The average of the standard error estimates (SEE), sample standard deviations (SSD) and the empirical mean square error (MSE) are also presented. The true value is 0.216.

(ψ₀, ψ₁)

Λ̃₁

Λ̂₁

{\hat{Λ}}_{1}^{S}

{\hat{Λ}}_{1}^{P}

({\hat{Λ}}_{1}^{S} + {\hat{Λ}}_{1}^{P}) / 2

(0.1, 0)

Estimate

.216

.281

.223

.216

.220

SEE

.074

.073

.074

SSD

.075

.073

\sqrt{MSE}

.075

.098

.073

(0.3, 0)

Estimate

.217

.411

.235

.214

.225

SEE

.097

.088

.097

SSD

.099

.089

.091

.095

.092

\sqrt{MSE}

.099

.215

.093

.095

.093

(0.5, 0)

Estimate

.214

.540

.249

.209

.229

SEE

.129

.102

.129

SSD

.127

.101

.110

.119

.113

\sqrt{MSE}

.127

.339

.115

.119

.114

(0.5, −0.5)

Estimate

.214

.390

.224

.215

.219

SEE

.091

.083

.091

SSD

.092

.083

.088

.090

.089

\sqrt{MSE}

.092

.193

.088

.090

.089

(0.5, −0.1)

Estimate

.214

.505

.241

.212

.226

SEE

.118

.098

.118

SSD

.116

.097

.104

.111

.106

\sqrt{MSE}

.116

.304

.107

.111

.107

The naive Λ̃₁, the constrained Λ̂₁, the SUP ${\hat{Λ}}_{1}^{S}$ and the PAV ${\hat{Λ}}_{1}^{P}$ estimator