. 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 3.

Simulation means for various estimators of the cumulative type 1 failure hazards at time 7 in the discrete 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 0.305.

(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

.306

.318

.312

.299

.306

SEE

.104

.103

.104

SSD

.107

.100

.102

.104

.103

\sqrt{MSE}

.107

.101

.103

.104

.103

(0.3, 0)

Estimate

.300

.335

.317

.285

.301

SEE

.137

.124

.137

SSD

.134

.115

.121

.129

.123

\sqrt{MSE}

.134

.119

.121

.130

.123

(0.5, 0)

Estimate

.299

.368

.333

.276

.304

SEE

.181

.142

.181

SSD

.182

.145

.157

.175

.163

\sqrt{MSE}

.182

.158

.159

.178

.163

(0.5, −0.5)

Estimate

.302

.312

.304

.301

.303

SEE

.105

.102

.105

SSD

.108

.102

.106

.107

\sqrt{MSE}

.108

.102

.106

.107

(0.5, −0.1)

Estimate

.300

.347

.320

.290

.305

SEE

.152

.131

.152

SSD

.154

.130

.139

.147

.141

\sqrt{MSE}

.153

.136

.140

.148

.141

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