Asymptotic bias of normal‐distribution‐based maximum likelihood estimates of moderation effects with data missing at random

2018 ◽  
Vol 72 (2) ◽  
pp. 334-354 ◽  
Author(s):  
Qian Zhang ◽  
Ke‐Hai Yuan ◽  
Lijuan Wang
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Missing At Random ◽  
Maximum Likelihood Estimates ◽  
Asymptotic Bias ◽  
Moderation Effects ◽  
Data Missing

AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

scholarly journals Modeling Observations with a Detection Limit using a Truncated Normal Distribution with Censoring

2020 ◽  
Author(s):  
Justin R. Williams ◽  
Hyung-Woo Kim ◽  
Catherine M. Crespi
Keyword(s):  
Detection Limit ◽  
Maximum Likelihood ◽  
Normal Distribution ◽  
Detection Limits ◽  
Intraocular Lenses ◽  
Maximum Likelihood Estimates ◽  
Quality Data ◽  
Type I ◽  
Truncated Normal Distribution ◽  
Truncated Normal

Abstract Background: When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative. Methods: We propose a method for estimating population mean and variance from censored observations that accounts for known domain restriction. The method finds maximum likelihood estimates assuming an underlying truncated normal distribution. Results: We show that our method, tcensReg, has lower bias, Type I error rates, and mean squared error than other methods commonly used for data with detection limits such as Tobit regression and single imputation under a range of simulation settings from mild to heavy censoring and truncation. We further demonstrate the consistency of the maximum likelihood estimators. We apply our method to analyze vision quality data collected from ophthalmology clinical trials comparing different types of intraocular lenses implanted during cataract surgery. All of the methods yield similar conclusions regarding non-inferiority, but estimates from the tcensReg method suggest that there may be greater mean differences and overall variability. Conclusions: In the presence of detection limits, our new method tcensReg provides a way to incorporate known domain restrictions in dependent variables that substantially improves inferences.

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