Feasible estimation in generalized structured models

Abstract

This article introduces a feasible estimation method for a large class of semi and nonparametric models. We present the family of generalized structured models which we wish to estimate. After highlighting the main idea of the theoretical smooth backfitting estimators, we introduce a general estimation procedure. We consider modifications and practical issues, and discuss inference, cross validation, and asymptotic theory applying the theoretical framework of Mammen and Nielsen (Biometrika 90: 551-566, 2003). An extensive simulation study shows excellent performance of our method. Furthermore, real data applications from environmetrics and biometrics demonstrate its usefulness.

Modeling heterogeneity: a praise for varying-coefficient models in causal analysis

“…Cai et al 2000), other spline methods (e.g. Chiang et al 2001), smooth backfitting (Mammen and Nielsen 2003;Roca-Pardinas and Sperlich 2010) and Bayesian structured additive models (Fahrmeir et al 2004) have been introduced as well. For most of these methods asymptotic theory has been provided.…”

“…Effective estimation of non-and semiparametric varying-coefficient models has been introduced in various articles, see Hastie and Tibshirani (1993) and Fan and Zhang (1999, 2000, including recursive estimation to improve efficiency (Cai et al 2000), estimation under measurement errors (Chiang et al 2001), models with generated regressors , generalized varying-coefficient models (Mammen and Nielsen 2003;Roca-Pardinas and Sperlich 2010) or additive varying coefficients (Yang et al 2006). The well-known time-varying-coefficient models for longitudinal data should be mentioned as well.…”

Varying Coefficient Regression Models: A Review and New Developments

“…() provided complete theory for the aforementioned smooth backfitting method. Roca‐Pardinas & Sperlich () added a link function to model . With a link function g , the model for the mean regression function is given by They presented a smooth backfitting algorithm but without theory.…”

Package wsbackfit for Smooth Backfitting Estimation of Generalized Structured Models

“…Mammen et al (1999) developed asymptotic theory for a modified version, the smooth backfitting (SB) estimator, under weaker assumptions on the data like the allowance for strong correlation of the covariates. Mammen and Nielsen (2003) extended this method to the general GSM class (1), and Roca-Pardiñas and Sperlich (2010) proposed a common algorithm for it. Many extensions have been developed, procedures for bandwidth selection (e.g., Mammen and Park, 2005), quantile regression (Lee et al, 2010), and further asymptotic theory for particular cases (see e.g., Yu et al, 2008, for GAM).…”