Identification and Estimation of Generalized Additive Partial Linear Models with Nonignorable Missing Response

The generalized additive partial linear models(GAPLM)have been widely used for flexiblemodeling of various types of response.In practice,missing data usually occurs in studies of economics,medicine,and public health.We address the problem of identifying and estimating GAPLM when the response variable is nonignorably missing.Three types of monotone missing data mechanism are assumed,including logistic model,probit model and complementary log-log model.In this situation,likelihood based on observed data may not be identifiable.In this article,we show that the parameters of interest are identifiable under very mild conditions,and then construct the estimators of the unknown parameters and unknown functions based on a likelihood-based approach by expanding the unknown functions as a linear combination of polynomial spline functions.We establish asymptotic normality for the estimators of the parametric components.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to the household income dataset from the Chinese Household Income Project Survey 2013.

Neural partially linear additive model

Interpretability has drawn increasing attention in machine learning.Most works focus on post-hoc explanations rather than building a self-explaining model.So,we propose a Neural Partially Linear Additive Model(NPLAM),which automatically distinguishes insignificant,linear,and nonlinear features in neural networks.On the one hand,neural network construction fits data better than spline function under the same parameter amount;on the other hand,learnable gate design and sparsity regular-term maintain the ability of feature selection and structure discovery.We theoretically establish the generalization error bounds of the proposed method with Rademacher complexity.Experiments based on both simulations and real-world datasets verify its good performance and interpretability.

Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters

This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.