Table 4.

Simulation means for various estimators of the cumulative type 1 failure hazards at time 7 in the discrete setting with a sample size n = 500 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	${\widehat{\mathit{\Lambda }}}_1^S$	${\widehat{\mathit{\Lambda }}}_1^P$	$({\widehat{\mathit{\Lambda }}}_1^S+{\widehat{\mathit{\Lambda }}}_1^P)/2$
(0.1, 0)	Estimate	.302	.302	.302	.302	.302
	SEE	.047	.046	.047	.047	.047
	SSD	.045	.045	.045	.045	.045
	$\sqrt{\text{MSE}}$	.045	.045	.045	.045	.045
(0.3, 0)	Estimate	.305	.307	.306	.303	.304
	SEE	.061	.056	.061	.061	.061
	SSD	.060	.059	.059	.060	.060
	$\sqrt{\text{MSE}}$	.060	.059	.059	.060	.059
(0.5, 0)	Estimate	.307	.316	.312	.300	.306
	SEE	.081	.064	.081	.081	.081
	SSD	.082	.076	.078	.083	.080
	$\sqrt{\text{MSE}}$	.082	.077	.078	.083	.080
(0.5, −0.5)	Estimate	.302	.302	.302	.302	.302
	SEE	.047	.046	.047	.047	.047
	SSD	.047	.046	.046	.046	.046
	$\sqrt{\text{MSE}}$	.047	.046	.046	.047	.047
(0.5, −0.1)	Estimate	.304	.308	.306	.303	.304
	SEE	.068	.059	.068	.068	.068
	SSD	.068	.065	.067	.068	.067
	$\sqrt{\text{MSE}}$	.068	.065	.067	.068	.067

The naive Λ̃₁, the constrained Λ̂₁, the SUP ${\widehat{\mathit{\Lambda }}}_1^S$ and the PAV ${\widehat{\mathit{\Lambda }}}_1^P$ estimator