Paper Info
Title
A Note On Parameters Estimation For Nonlinear Wiener Processes With Measurement Errors
Abstract
The nonlinear Wiener process has been widely used as a model for the degradation process. This note concerns parameters estimation of nonlinear Wiener processes with measurement errors (WPME) by the maximum likelihood estimation method. Firstly, we prove a rule that the estimated results based on the sample likelihood function developed through observations at each point are equal to the results from the first differences of the observations. This rule indicates that for reducing computation complexity the first differences of the observations may develop the sample likelihood function. Then we present a simple method to calculate the determinant and the inverse matrix of the covariance matrix of the WPME. This simple method could avoid the overflow error when calculating the determinant of the covariance matrix and the case that the inverse matrix is close to be singular, which could result in wrong estimation results. Secondly, we highlight the unit-specific assumption, which has a significant impact on parameters estimation but has been neglected in many papers. Then, we propose a modified expectation maximization algorithm for parameters estimation with random effects. Finally, to demonstrate the application and superiority of the proposed method, we provide a numerical example and a case study with comparison to several representative methods in the literature.
Year
DOI
Venue
2019
10.1109/ACCESS.2019.2954717
IEEE ACCESS
Keywords
DocType
Volume
Degradation model, maximum likelihood estimation, Wiener process, measurement error, nonlinear, expectation maximization algorithm
Journal
7
ISSN
Citations 
PageRank 
2169-3536
0
0.34
References 
Authors
0
5
Name
Order
Citations
PageRank
Shengjin Tang112.04
Chuanqiang Yu200.34
Xiaoyan Sun300.68
Hongdong Fan400.68
Xiao-Sheng Si562346.17