• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.69-78
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• 2019

A structured model with both single-index and varying coefficients is a powerful tool in modeling high dimensional data. It has been widely used because the single-index can overcome the curse of dimensionality and varying coefficients can allow nonlinear interaction effects in the model. For high dimensional index vectors, variable selection becomes an important question in the model building process. In this paper, we propose an efficient estimation and a variable selection method based on a smoothing spline approach in a partially linear single-index-coefficient regression model. We also propose an efficient algorithm for simultaneously estimating the coefficient functions in a data-adaptive lower-dimensional approximation space and selecting significant variables in the index with the adaptive LASSO penalty. The empirical performance of the proposed method is illustrated with simulated and real data examples.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.385-407
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• 2010

To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.

• Smart Structures and Systems
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• v.29 no.1
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• pp.41-51
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• 2022

Cables are critical components of cable-stayed bridges. A structural health monitoring system provides real-time cable tension recording for cable health monitoring. However, the measurement data involve multiple sources of variability, i.e., varying environmental and operational factors, which increase the complexity of cable condition monitoring. In this study, a one-class classification method is developed for cable condition assessment using Bayesian factor analysis (FA). The single-peaked vehicle-induced cable tension is assumed to be relevant to vehicle positions and weights. The Bayesian FA is adopted to establish the correlation model between cable tensions and vehicles. Vehicle weights are assumed to be latent variables and the influences of different transverse positions are quantified by coefficient parameters. The Bayesian theorem is employed to estimate the parameters and variables automatically, and the damage index is defined on the basis of the well-trained model. The proposed method is applied to one cable-stayed bridge for cable damage detection. Significant deviations of the damage indices of Cable SJS11 were observed, indicating a damaged condition in 2011. This study develops a novel method to evaluate the health condition of individual cable using the FA in the Bayesian framework. Only vehicle-induced cable tensions are used and there is no need to monitor the vehicles. The entire process, including the data pre-processing, model training and damage index calculation of one cable, takes only 35 s, which is highly efficient.