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Local CQR Smoothing: An Efficient and Safe Alternative to Local Polynomial Regression.

ABSTRACT: Local polynomial regression is a useful nonparametric regression tool to explore fine data structures and has been widely used in practice. In this paper, we propose a new nonparametric regression technique called local composite-quantile-regression (CQR) smoothing in order to further improve local polynomial regression. Sampling properties of the proposed estimation procedure are studied. We derive the asymptotic bias, variance and normality of the proposed estimate. Asymptotic relative efficiency of the proposed estimate with respect to the local polynomial regression is investigated. It is shown that the proposed estimate can be much more efficient than the local polynomial regression estimate for various non-normal errors, while being almost as efficient as the local polynomial regression estimate for normal errors. Simulation is conducted to examine the performance of the proposed estimates. The simulation results are consistent with our theoretical findings. A real data example is used to illustrate the proposed method.

SUBMITTER: Kai B

PROVIDER: S-EPMC2958780 | biostudies-literature | 2010 Jan

REPOSITORIES: biostudies-literature

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Local CQR Smoothing: An Efficient and Safe Alternative to Local Polynomial Regression.

Kai Bo B Li Runze R Zou Hui H

Journal of the Royal Statistical Society. Series B, Statistical methodology 20100101 1

Local polynomial regression is a useful nonparametric regression tool to explore fine data structures and has been widely used in practice. In this paper, we propose a new nonparametric regression technique called local composite-quantile-regression (CQR) smoothing in order to further improve local polynomial regression. Sampling properties of the proposed estimation procedure are studied. We derive the asymptotic bias, variance and normality of the proposed estimate. Asymptotic relative efficie ...[more]

PMID: 20975930

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Project description:Malaria is one of the most severe problems faced by the world even today. Understanding the causative factors such as age, sex, social factors, environmental variability etc. as well as underlying transmission dynamics of the disease is important for epidemiological research on malaria and its eradication. Thus, development of suitable modeling approach and methodology, based on the available data on the incidence of the disease and other related factors is of utmost importance. In this study, we developed a simple non-linear regression methodology in modeling and forecasting malaria incidence in Chennai city, India, and predicted future disease incidence with high confidence level. We considered three types of data to develop the regression methodology: a longer time series data of Slide Positivity Rates (SPR) of malaria; a smaller time series data (deaths due to Plasmodium vivax) of one year; and spatial data (zonal distribution of P. vivax deaths) for the city along with the climatic factors, population and previous incidence of the disease. We performed variable selection by simple correlation study, identification of the initial relationship between variables through non-linear curve fitting and used multi-step methods for induction of variables in the non-linear regression analysis along with applied Gauss-Markov models, and ANOVA for testing the prediction, validity and constructing the confidence intervals. The results execute the applicability of our method for different types of data, the autoregressive nature of forecasting, and show high prediction power for both SPR and P. vivax deaths, where the one-lag SPR values plays an influential role and proves useful for better prediction. Different climatic factors are identified as playing crucial role on shaping the disease curve. Further, disease incidence at zonal level and the effect of causative factors on different zonal clusters indicate the pattern of malaria prevalence in the city. The study also demonstrates that with excellent models of climatic forecasts readily available, using this method one can predict the disease incidence at long forecasting horizons, with high degree of efficiency and based on such technique a useful early warning system can be developed region wise or nation wise for disease prevention and control activities.

Dataset Information

Local CQR Smoothing: An Efficient and Safe Alternative to Local Polynomial Regression.

Publications

Local CQR Smoothing: An Efficient and Safe Alternative to Local Polynomial Regression.

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