• 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.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.305-312
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• 2015

We extend a generalized partially linear single-index model and newly define a generalized partially double-index model (GPDIM). The philosophy of sufficient dimension reduction is adopted in GPDIM to estimate unknown coefficient vectors in the model. Subsequently, various combinations of popular sufficient dimension reduction methods are constructed with the best combination among many candidates determined through a bootstrapping procedure that measures distances between subspaces. Distinguishing values are newly defined to match the estimates to the corresponding population coefficient vectors. One of the strengths of the proposed model is that it can investigate the appropriateness of GPDIM over a single-index model. Various numerical studies confirm the proposed approach, and real data application are presented for illustration purposes.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• 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.

• The Journal of Asian Finance, Economics and Business
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• v.9 no.7
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• pp.153-171
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• 2022

To measure economic performance, customer satisfaction indices are constructed. This study proposes an index for banking and telecom, a significant evaluative system for comparing and enhancing customer satisfaction across the industries. The study suggests and examines amendments and improvements to the prior indices and incorporates ignored indicators to propose a punier index for Pakistan. The study is a pioneer in integrating online and offline indices into a single comprehensive model. The study is enriched by the Theory of Reasoned Action and Technological Acceptance Model. A sample of 320 respondents was used. The sample was divided based on gender and marital status. To authenticate the theoretical model, PLS-SEM was applied. We discovered nine latent variables that define customer satisfaction and conclude that a single model can be utilized for e-commerce enterprises as well. The index scores are comparable to the American index for banking and the Turkish index for telecom. Multi-group analysis (MGA) was used to comprehend the differences among the groups. This reveals that customization, design, reliability, and responsiveness induce satisfaction in telecom male and married customers. For the banking industry, the difference exists in complaint handling, customization, corporate image, perceived price, reliability, responsiveness, sentiments, convenience, and security to satisfaction links, image and complaint handling to loyalty links.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.83-126
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• 2005

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. Here we propose a nonparametric estimation approach that combines wavelet methods for non-equispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.

• Proceedings of the Safety Management and Science Conference
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• 2011.04a
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• pp.701-705
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• 2011

The paper reviews Cronbaha's coefficient to measure a single source of error. On the contrary to classical measurement theory, the generalizability study can be used in the social survey design to calculate Generalizability Index (GI) and Dependability Index (DI) for measuring multiple sources of errors of behavior evaluation. The study proposes application guidelines to implement R:($A{\times}B$) mixed models that are composed of random factor and fixed factor.

• Journal of Families and Better Life
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• v.20 no.1
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• pp.45-56
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• 2002

The main purposes of this article are to introduce the theoretical backgrounds and empirical application methods of two different Models for the function of expenditure, and to compare the goodness-o(-fit of the two models: a single-equation model and a complete-system-of-demand-equation model. For the empirical analysis of the single-equation model, a linear formula and a double-leg formula were employed. In order to test the complete-system-of-demand-equation model empirically, the \"Linear Approximation/Almost Ideal Demand System (LA/AIDS)" was used. The independent variables were the total living expense and expenditure categories Price index. The data used in this study were obtained from the quarterly statistics of "The Annual Report on the Urban Family Income and Expenditure Survey (Dosigagyeyonbo)" and "The Annual Report on the Consumer Price Index (Sobijamulgajaryo)," for the years 1994 to 1997. The goodness-of-fit (R-square) was higher with the complete-system-of-demand-equation model than with the single-equation model for the budget share on food (excluding eating-out expenses) and for the share on cultural and recreational activities. However, there was no difference between the two models in terms of the proportion of the expenditure on automobile fuel.fuel.

• Transactions on Electrical and Electronic Materials
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• v.13 no.4
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• pp.196-199
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• 2012

CdS thin film was prepared on glass substrate by chemical bath deposition in an alkaline solution. The optical properties of CdS thin film were investigated using spectroscopic ellipsometry. The real (${\varepsilon}_1$) and imaginary (${\varepsilon}_2$) parts of the complex dielectric function ${\varepsilon}(E)={\varepsilon}_1(E)+i{\varepsilon}_2(E)$, the refractive index n(E), and the extinction coefficient k(E) of CdS thin film were obtained from spectroscopic ellipsometry. The normal-incidence reflectivity R(E) and absorption coefficient ${\alpha}(E)$ of CdS thin film were obtained using the refractive index and extinction coefficient. The critical points $E_0$ and $E_1$ of CdS thin film were shown in spectra of the dielectric function and optical constants of refractive index, extinction coefficient, normal-incidence reflectivity, and absorption coefficient. The dispersion of refractive index was analyzed by the Wemple-DiDomenico single-oscillator model.

• Steel and Composite Structures
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• v.37 no.5
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• pp.621-632
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• 2020

This research deals with the study of vibrational behavior of armchair and zigzag single-walled carbon nanotubes invoking extended Love shell theory. The effects of different physical and material parameters on the fundamental frequencies are investigated. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. To discretize the governing equation in eigen-value form, wave propagation approach is developed. Complex exponential functions have been used and the axial model depends on boundary condition that has been described at the edges of carbon nanotubes to calculate the axial modal dependence. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes and current results shows a good stability with comparison of other studies.