Variable selection for additive partial linear quantile regression with missing covariates

Quantile partially linear additive model for data with dropouts and an application to modeling cognitive decline

The National Alzheimer's Coordinating Center Uniform Data Set includes test results from a battery of cognitive exams. Motivated by the need to model the cognitive ability of low-performing patients we create a composite score from ten tests and propose to model this score using a partially linear quantile regression model for longitudinal studies with non-ignorable dropouts. Quantile regression allows for modeling non-central tendencies. The partially linear model accommodates nonlinear relationships between some of the covariates and cognitive ability. The data set includes patients that leave the study prior to the conclusion. Ignoring such dropouts will result in biased estimates if the probability of dropout depends on the response. To handle this challenge, we propose a weighted quantile regression estimator where the weights are inversely proportional to the estimated probability a subject remains in the study. We prove that this weighted estimator is a consistent and efficient estimator of both linear and nonlinear effects.

Economic Growth and Environmental Quality: Analysis of Government Expenditure and the Causal Effect

Environmental expenditures (EX) are made by the government and industries which are either long-term or short-term investments. The principal target of EX is to eliminate environmental hazards, promote sustainable natural resources, and improve environmental quality (EQ). Thus, this study looks at the impact of economic growth (EG), and government finance expenditure (GEX) on EQ in Northern Africa and Southern Africa (NASA) republics from 2000-2016. The panel quantile regression (PQR) and panel vector autoregressive (PVAR) model in a generalized method of moment framework (GMM) were employed as a framework. The PQR results show that; (i) In Northern republics, GEX had a significant positive effect on EQ at 25%, 50%, and 75% quantiles levels. (ii) In the Southern republics, GEX had a significant negative impact on EQ at 25%. Moreover, the PVAR through the GMM established that EG and GEX are significantly positive while the parameter for CO₂ is insignificant and negative in the North. However, in the South, GEX and CO₂ were statistically significant, while EG positively impacts EQ. Lastly, the granger causality report in North indicates uni-directional causation running from LNGEX → LNGDPpc, LNCO₂ → LNGDPpc, LNFF → LNGEX, and LNFDI → LNGEX. Similarly, there is uni-directional causation in South republics from LNGEX → LNGDPpc, LNCO₂ → LNGEX, and LNFDI → LNGEX.

The impact of banks' financial performance on environmental performance in Africa

To better understand Africa's banks and the environment, this study investigates the impact of financial performance on environmental performance in Africa. We examined financial performance, environmental performance, and some control indicators dated from 2000 to 2016 by applying panel quantile regression and panel vector autoregressive techniques. Our results indicate that (i) in North African countries, carbon emission had a significant negative impact on financial performance on the 25th quantile and (ii) in the South, carbon emission had a statistically positive impact on financial performance on the 25th and 50th quantiles with the marginal effect increases from the lower quantile to the highest quantile. Also, bank deposits statistically negatively impacted financial performance on the 25th and 50th quantiles for both North and South economies. The dynamic panel quantile results show dissimilar effects at different quantiles. Also, the panel vector autoregressive results show that in North Africa carbon emission had a positive impact. Our results validate the stability test of the panel vector autoregressive model. The granger causality results in the North show a bilateral causal link between carbon emission and bank credit, carbon emission, and bank deposit. Since sustainability has become one of our era's most thorny issues, this paper provides extensive policy directives to assist African nations in boosting a greener future.

Variable selection for ultra-high dimensional quantile regression with missing data and measurement error

In this paper, we consider variable selection for ultra-high dimensional quantile regression model with missing data and measurement errors in covariates. Specifically, we correct the bias in the loss function caused by measurement error by applying the orthogonal quantile regression approach and remove the bias caused by missing data using the inverse probability weighting. A nonconvex Atan penalized estimation method is proposed for simultaneous variable selection and estimation. With the proper choice of the regularization parameter and under some relaxed conditions, we show that the proposed estimate enjoys the oracle properties. The choice of smoothing parameters is also discussed. The performance of the proposed variable selection procedure is assessed by Monte Carlo simulation studies. We further demonstrate the proposed procedure with a breast cancer data set.