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Duration Models
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
Both semi-parametric and fully parametric hazard-based models have been widely cited in the literature. Fully parametric models assume a distribution of duration times (e.g., Weibull, exponential, and so on) and also have a parametric assumption on the functional form of the explanatory variables’ influence on the hazard function (usually EXP(βX) as discussed previously). Semi-parametric models, in contrast, are more general in that they do not assume a duration-time distribution, although they do retain the parametric assumption of the explanatory variable influence.
Ageing Intensity Function for Conditionally Specified Models
Published in American Journal of Mathematical and Management Sciences, 2020
S. M. Sunoj, N. Unnikrishnan Nair, Asok K. Nanda, R. S. Rasin
In survival studies, the most widely used semi-parametric model is the Cox proportional hazard rates (PHR) model. Let and be two bivariate random vectors with joint probability density functions and and joint survival functions given by and respectively. Let us assume that the common support is for Also let and denote respectively the probability density function, the survival function and the hazard rate function of for Analogous to the proportional hazard rates model for univariate random variables, the random vectors and satisfy the conditional PHR model (see Sankaran and Sreeja (2007)) when, for where is a nonnegative function of tj.
A multi-model ensemble approach to process optimization considering model uncertainty
Published in Journal of Industrial and Production Engineering, 2018
To construct a multi-model ensemble, we considered three individual modeling techniques in this paper: semi-parametric, kriging, and radial basis function (RBF). These models were chosen as the three members of the ensemble, which is based on the different characteristics of each model. Unlike the parametric and nonparametric modeling techniques, the semi-parametric model does not require a large sample size and tends to work well when the sample size is small [17]. Lee and Kang [18] showed that the kriging method performs better than parametric techniques in terms of approximation capability since it provides an accurate prediction of a highly nonlinear function. Jin et al. [19] verified that the RBF model performs better than parametric and kriging models in terms of predictive accuracy and robustness by studying the effect of sample size on the performance of model prediction.
Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis
Published in Technometrics, 2018
Yimeng Xie, Caleb B. King, Yili Hong, Qingyu Yang
On another side, there has been tremendous statistical research in nonparametric methods, although the current industrial practice is still to use application-specific parametric models to describe ADDT data. In this article, we aim to bridge this gap between the statistical research and current industrial practice. Instead of a case-by-case parametric modeling approach, we propose a general and flexible semiparametric model to describe ADDT data, which is new to the ADDT data analysis literature. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and from performing extrapolations for predictions at the use condition. To overcome those challenges, the semiparametric model consists of a nonparametric model for the degradation path and a parametric form for the accelerating-variable effect. To preserve the monotonic nature of many degradation paths, the nonparametric model portion will be constructed based on monotonic spline methods. For the parametric model portion, commonly used models, such as the Arrhenius relationship for temperature, will be used for extrapolation. Parameter estimation and inference procedures will also be developed. Through application demonstration and simulations, we show that the proposed semiparametric model is more flexible, applicable to a wide range of applications, and is more robust to model misspecification. An R package “ADDT” (Hong et al. 2016) is also developed, and the use of the R package is illustrated in Jin et al. (2017). The developed method can be useful for industrial standards, such as UL746B (2013), due to its flexibility and robustness, and software readiness for ADDT data analysis.