scholarly journals Estimation for Varying Coefficient Models with Hierarchical Structure

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 132
Author(s):  
Feng Li ◽  
Yajie Li ◽  
Sanying Feng
Keyword(s):  
Variable Selection ◽  
Hierarchical Structure ◽  
Kernel Method ◽  
Real Data ◽  
Unknown Coefficient ◽  
Nonparametric Model ◽  
Finite Sample ◽  
Oracle Properties ◽  
Varying Coefficient ◽  
The Hierarchical Structure

The varying coefficient (VC) model is a generalization of ordinary linear model, which can not only retain strong interpretability but also has the flexibility of the nonparametric model. In this paper, we investigate a VC model with hierarchical structure. A unified variable selection method for VC model is proposed, which can simultaneously select the nonzero effects and estimate the unknown coefficient functions. Meanwhile, the selected model enforces the hierarchical structure, that is, interaction terms can be selected into the model only if the corresponding main effects are in the model. The kernel method is employed to estimate the varying coefficient functions, and a combined overlapped group Lasso regularization is introduced to implement variable selection to keep the hierarchical structure. It is proved that the proposed penalty estimators have oracle properties, that is, the coefficients are estimated as well as if the true model were known in advance. Simulation studies and a real data analysis are carried out to examine the performance of the proposed method in finite sample case.

scholarly journals Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jinghua Zhang ◽  
Liugen Xue
Keyword(s):  
Variable Selection ◽  
Longitudinal Data ◽  
Linear Models ◽  
Selection Procedure ◽  
Real Data ◽  
Finite Sample ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Quadratic Inference Function ◽  
Quadratic Inference Functions

Semiparametric generalized varying coefficient partially linear models with longitudinal data arise in contemporary biology, medicine, and life science. In this paper, we consider a variable selection procedure based on the combination of the basis function approximations and quadratic inference functions with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency, sparsity, and asymptotic normality of the resulting estimators. The finite sample performance of the proposed methods is evaluated through extensive simulation studies and a real data analysis.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

scholarly journals Extending Goldberg’s bass-ackwards method for delineating hierarchical structural models in individual differences data

2020 ◽  
Author(s):  
Miriam K. Forbes
Keyword(s):  
Individual Differences ◽  
Hierarchical Structure ◽  
Traditional Approach ◽  
Structural Models ◽  
Real Data ◽  
Current Approach ◽  
Path Coefficients ◽  
The Hierarchical Structure ◽  
Basic Code ◽  
Multiple Levels

Goldberg’s (2006) bass-ackwards approach to elucidating the hierarchical structure of individual differences data has been used widely to improve our understanding of the relationships among constructs of varying levels of granularity. The traditional approach has been to extract a single component on the first level of the hierarchy, two components on the second level, and so on, treating the correlations between the components on adjoining levels akin to path coefficients in a hierarchical structure. This article proposes three modifications to the current approach with a particular focus on examining associations among all levels of the hierarchy: 1) identify and remove redundant components that perpetuate through multiple levels of the hierarchy; 2) (optionally) identify and remove artefactual components; and 3) plot the strongest component correlations among the remaining components to identify their hierarchical associations. Together these steps can offer a simpler and more complete picture of the underlying hierarchical structure among a set of observed variables. The rationale for each step is described, illustrated in a hypothetical example, and then applied in real data with specific methodological recommendations. The results are compared to the traditional bass-ackwards approach, and basic code is provided to apply the proposed modifications in other data.

scholarly journals PQMLE of a Partially Linear Varying Coefficient Spatial Autoregressive Panel Model with Random Effects

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2057
Author(s):  
Shuangshuang Li ◽  
Jianbao Chen ◽  
Danqing Chen
Keyword(s):  
Random Effects ◽  
Spatial Data ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Finite Sample ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Panel Model ◽  
Spatial Autoregressive ◽  
Quasi Maximum Likelihood

This article deals with asymmetrical spatial data which can be modeled by a partially linear varying coefficient spatial autoregressive panel model (PLVCSARPM) with random effects. We constructed its profile quasi-maximum likelihood estimators (PQMLE). The consistency and asymptotic normality of the estimators were proved under some regular conditions. Monte Carlo simulations implied our estimators have good finite sample performance. Finally, a set of asymmetric real data applications was analyzed for illustrating the performance of the provided method.

VARIABLE SELECTION FOR PARTIALLY LINEAR VARYING COEFFICIENT QUANTILE REGRESSION MODEL

2013 ◽  
Vol 06 (03) ◽  
pp. 1350015 ◽  
Author(s):  
JIANG DU ◽  
ZHONGZHAN ZHANG ◽  
ZHIMENG SUN
Keyword(s):  
Variable Selection ◽  
Selection Procedure ◽  
Adaptive Lasso ◽  
Regularity Conditions ◽  
Finite Sample ◽  
Unknown Parameters ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Variable Selection Procedure ◽  
Quantile Loss

In this paper, we propose a variable selection procedure for partially linear varying coefficient model under quantile loss function with adaptive Lasso penalty. The functional coefficients are estimated by B-spline approximations. The proposed procedure simultaneously selects significant variables and estimates unknown parameters. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, we show that the proposed procedure can be as efficient as the Oracle estimator, and derive the optimal convergence rate of the functional coefficients. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Efficient robust doubly adaptive regularized regression with applications

2018 ◽  
Vol 28 (7) ◽  
pp. 2210-2226 ◽  
Author(s):  
Rohana J Karunamuni ◽  
Linglong Kong ◽  
Wei Tu
Keyword(s):  
Variable Selection ◽  
Breakdown Point ◽  
Practical Implementation ◽  
Regularized Regression ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Oracle Properties ◽  
Adaptive Weights ◽  
Monte Carlo Studies ◽  
Finite Sample Breakdown Point

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

scholarly journals Adjusted Empirical Likelihood for Varying Coefficient Partially Linear Models with Censored Data

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Peixin Zhao
Keyword(s):  
Censored Data ◽  
Empirical Likelihood ◽  
Linear Models ◽  
Real Data ◽  
Partially Linear Models ◽  
Finite Sample ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Adjusted Empirical Likelihood ◽  
Chi Squared

By constructing an adjusted auxiliary vector ingeniously, we propose an adjusted empirical likelihood ratio function for the parametric components of varying coefficient partially linear models with censored data. It is shown that its limiting distribution is standard central chi-squared. Then the confidence intervals for the parametric components are constructed. A simulation study and a real data analysis are undertaken to assess the finite sample performance of the proposed method.

Parafia unicka w Rachaniach do 1811 roku/ The Uniate Parish in Rachanie until 1811

2012 ◽  
Vol 67 (2) ◽  
Author(s):  
Janusz Adam Frykowski
Keyword(s):  
Hierarchical Structure ◽  
Geographical Location ◽  
Historical Sources ◽  
Holy Communion ◽  
The Hierarchical Structure ◽  
History Of ◽  
The Church ◽  
Ancillary Equipment

AbstractThe following paper depicts the history of Saint Simeon Stylites Uniate Parish in Rachanie since it became known in historical sources until 1811- that is the time it ceased to be an independent church unit. The introduction of the article contains the geographical location of the parish, its size and the position within the hierarchical structure of the Church. Having analysed post-visit inspection protocols left by Chelm Bishops, the appearance as well as fittings and ancillary equipment of the church in Rachanie in that particular period are reported. Moreover, the list of 4 local clergymen is recreated and their benefice is determined. As far as possible, both the number of worshipers and the number of Holy Communion receivers is determined.

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