Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates

By Li Wang, Lan Xue, Annie Qu, Hua Liang. 2014

71 citations recorded by the source corpus.

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.

Subfields: Artificial Intelligence, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lijian Yang
2. Li Wang
3. Raymond K. Wong
4. Yehua Li
5. Shan Yu
6. Chenhui Liu
7. Guannan Wang
8. Shujie Ma

In Statistics and Probability

1. Li Wang
2. Lijian Yang
3. Raymond K. Wong
4. Guannan Wang
5. Shan Yu
6. Chenhui Liu
7. Yehua Li
8. Shujie Ma

Citations in the corpus

• Partially Linear Functional Additive Models for Multivariate Functional Data (2018, methodology): “As shown in our proof,V 1 = cov{n1/2(ε, w̃)n}, and M−1V 1M−1 is the typical asymptotic covariance matrix of γ̂ in classic literature of partially linear additive model (Wang et al. 2014), where ζ is directly observed.”
• Estimation and Inference for Generalized Geoadditive Models (2020, background): “This ensures that the spline functions are centered (see Xue and Yang 2006; Wang and Yang 2007; Wang et al. 2014).”