Incomplete covariates data in generalized linear models |
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| Institution: | 1. Operations Management, Quantitative Methods and Information Systems Area, Indian Institute of Management Udaipur, Udaipur 313001, Rajasthan, India;2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;1. Amsterdam School of Economics, University of Amsterdam, The Netherlands;2. Faculty of Actuarial Science and Insurance, Cass Business School, City University London, United Kingdom;3. RiskLab, Department of Mathematics, ETH Zurich, Switzerland;1. Jiangsu Laboratory of Lake Environment Remote Sensing Technologies, Huaiyin Institute of Technology, Huaian, China;2. Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, China;1. Takeda Oncology Co., Cambridge, MA, United States;2. Department of Statistics, University of Virginia, Charlottesville, VA, United States;3. Department of Preventive Medicine, Northwestern University, Chicago, IL, United States |
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| Abstract: | We consider regression analysis when part of covariates are incomplete in generalized linear models. The incomplete covariates could be due to measurement error or missing for some study subjects. We assume there exists a validation sample in which the data is complete and is a simple random subsample from the whole sample. Based on the idea of projection-solution method in Heyde (1997, Quasi-Likelihood and its Applications: A General Approach to Optimal Parameter Estimation. Springer, New York), a class of estimating functions is proposed to estimate the regression coefficients through the whole data. This method does not need to specify a correct parametric model for the incomplete covariates to yield a consistent estimate, and avoids the ‘curse of dimensionality’ encountered in the existing semiparametric method. Simulation results shows that the finite sample performance and efficiency property of the proposed estimates are satisfactory. Also this approach is computationally convenient hence can be applied to daily data analysis. |
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