Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using general...Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.展开更多
In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose a...In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.展开更多
This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） prop...This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.展开更多
In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero c...In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.展开更多
The coefficients of linear thermal expansions （CLEs） of magnetic elements Fe, Co and Ni were assessed from experimental information using theoretical models combined with MATLAB calculations. Model parameters can be...The coefficients of linear thermal expansions （CLEs） of magnetic elements Fe, Co and Ni were assessed from experimental information using theoretical models combined with MATLAB calculations. Model parameters can be determined accurately, and the assessed data are in good agreement with the experimental results. To facilitate the assessments, theories of thermal expansion were applied to separate CLEs into its nonmagnetic and magnetic components. The calculations of nonmagnetic contribution to CLEs were based on the modified Gruineisen- Debye model, in which the Debye temperature was regarded as an undetermined constant. In order to put the prediction of CLEs at the magnetic transition region on a sound physical basis, two kinds of theoretical models were innovatively used to calculate the magnetic contribution to CLEs, i.e., the Bragg-Williams model and the Fermi-Dirac distribution function. Model parameters were evaluated from experimental data using least square method. Detailed comparisons were made with the published experimental data and the calculated total CLEs. A satisfactory agreement is reached.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null d...In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to...In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.展开更多
BACKGROUND Chronic hepatitis B often progresses silently toward hepatocellular carcinoma(HCC),a leading cause of mortality worldwide.Early detection of HCC is crucial,yet challenging.AIM To investigate the role of dyn...BACKGROUND Chronic hepatitis B often progresses silently toward hepatocellular carcinoma(HCC),a leading cause of mortality worldwide.Early detection of HCC is crucial,yet challenging.AIM To investigate the role of dynamic changes in alkaline phosphatase to prealbumin ratio(APR)in hepatitis B progression to HCC.METHODS Data from 4843 patients with hepatitis B(January 2015 to January 2024)were analyzed.HCC incidence rates in males and females were compared using the log-rank test.Data were evaluated using Kaplan–Meier analysis.The Linear Mixed-Effects Model was applied to track the fluctuation of APR levels over time.Furthermore,Joint Modeling of Longitudinal and Survival data was employed to investigate the temporal relationship between APR and HCC risk.RESULTS The incidence of HCC was higher in males.To ensure the model’s normality assumption,this study applied a logarithmic transformation to APR,yielding ratio.Ratio levels were higher in females(t=5.26,P<0.01).A 1-unit increase in ratio correlated with a 2.005-fold higher risk of HCC in males(95%CI:1.653-2.431)and a 2.273-fold higher risk in females(95%CI:1.620-3.190).CONCLUSION Males are more prone to HCC,while females have higher APR levels.Despite no baseline APR link,rising APR indicates a higher HCC risk.展开更多
文摘Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1110111911126332)+2 种基金the National Social Science Foundation of China(Grant No.11CTJ004)the Natural Science Foundation of Guangxi Province(Grant No.2010GXNSFB013051)the Philosophy and Social Sciences Foundation of Guangxi Province(Grant No.11FTJ002)
文摘In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.
基金supported by the National Natural Science Funds for Distinguished Young Scholar (70825004)National Natural Science Foundation of China (NSFC) (10731010 and 10628104)+3 种基金the National Basic Research Program (2007CB814902)Creative Research Groups of China (10721101)Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics211 Project for Shanghai University of Financeand Economics (the 3rd phase)
文摘This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
文摘In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.
基金financially supported by China Postdoctoral Science Foundation(No.2009045110)
文摘The coefficients of linear thermal expansions （CLEs） of magnetic elements Fe, Co and Ni were assessed from experimental information using theoretical models combined with MATLAB calculations. Model parameters can be determined accurately, and the assessed data are in good agreement with the experimental results. To facilitate the assessments, theories of thermal expansion were applied to separate CLEs into its nonmagnetic and magnetic components. The calculations of nonmagnetic contribution to CLEs were based on the modified Gruineisen- Debye model, in which the Debye temperature was regarded as an undetermined constant. In order to put the prediction of CLEs at the magnetic transition region on a sound physical basis, two kinds of theoretical models were innovatively used to calculate the magnetic contribution to CLEs, i.e., the Bragg-Williams model and the Fermi-Dirac distribution function. Model parameters were evaluated from experimental data using least square method. Detailed comparisons were made with the published experimental data and the calculated total CLEs. A satisfactory agreement is reached.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
文摘In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.
文摘BACKGROUND Chronic hepatitis B often progresses silently toward hepatocellular carcinoma(HCC),a leading cause of mortality worldwide.Early detection of HCC is crucial,yet challenging.AIM To investigate the role of dynamic changes in alkaline phosphatase to prealbumin ratio(APR)in hepatitis B progression to HCC.METHODS Data from 4843 patients with hepatitis B(January 2015 to January 2024)were analyzed.HCC incidence rates in males and females were compared using the log-rank test.Data were evaluated using Kaplan–Meier analysis.The Linear Mixed-Effects Model was applied to track the fluctuation of APR levels over time.Furthermore,Joint Modeling of Longitudinal and Survival data was employed to investigate the temporal relationship between APR and HCC risk.RESULTS The incidence of HCC was higher in males.To ensure the model’s normality assumption,this study applied a logarithmic transformation to APR,yielding ratio.Ratio levels were higher in females(t=5.26,P<0.01).A 1-unit increase in ratio correlated with a 2.005-fold higher risk of HCC in males(95%CI:1.653-2.431)and a 2.273-fold higher risk in females(95%CI:1.620-3.190).CONCLUSION Males are more prone to HCC,while females have higher APR levels.Despite no baseline APR link,rising APR indicates a higher HCC risk.
