Model selection and model averaging for semiparametric partially linear models with missing data

Model selection and model averaging for analysis of truncated and censored data with measurement error

“…Interestingly, for both the naive approach and the proposed method, using FIC tends to result in smaller RMSEs than using AIC or BIC under our simulation settings. While there is no rigorous theory to show this is always the case, such a phenomenon was also being observed by other authors such as [21], [22], [30], and [31]. Furthermore, the model averaging estimators, sAIC, sBIC and sFIC, are comparable to their counterparts, AIC, BIC and FIC, respectively, and sFIC outperforms both sAIC and sBIC under the settings we consider.…”

A robust model averaging approach for partially linear models with responses missing at random

“…The bandwidth $$$ {h}_l $$$ is simply set to be $$$ \mathrm{std}\left({T}_1\right){n}^{-1/5} $$$. In fact this design is similar to Zeng et al (2019) in that the nonlinear part of each candidate model is fixed. However, we allow the number of candidate models to increase as the sample size increases while the number of candidate models in Zeng et al (2019) is fixed.…”

“…Example In this example, we analyzed the Ragweed Pollen Level (RPL) dataset. This dataset was collected in Kalamazoo, Michigan during the ragweed season from 1991 to 1994, and has been used in many exist literature (see, e.g., Ruppert et al, 2003; Ni et al, 2009; Zeng et al, 2019). The raw RPL dataset totally has $$$ n=334 $$$ daily observations of ragweed pollen level (grains/$$$ {\mathrm{m}}^3 $$$) and four relevant impact variables.…”

“…Clearly, the local misspecification framework is unrealistic and not very applicable. Zeng et al (2019) developed FIC model averaging procedure (Claeskens & Hjort, 2003) for PLMs with responses missing at random based on nonparametric kernel regression technique and imputation method. However, Zeng et al (2019) considered that the nonlinear part of each candidate model is the same but allowing only the linear part to vary between candidate models.…”

“…Zeng et al (2019) developed FIC model averaging procedure (Claeskens & Hjort, 2003) for PLMs with responses missing at random based on nonparametric kernel regression technique and imputation method. However, Zeng et al (2019) considered that the nonlinear part of each candidate model is the same but allowing only the linear part to vary between candidate models. To some extend, this is essentially the same as the model averaging approaches for linear models.…”