Estimating population size of heterogeneous populations with large data sets and a large number of parameters

Abstract

A generalized partial linear regression model is proposed to estimate population size at a specific time from multiple lists of a time-varying and heterogeneous population. The challenge is that we have millions of records and hundreds of parameters for a long period of time. This presents a challenge for data analysis, mainly due to the limitation of computer memory, computational convergence and infeasibility. In the paper, an analytical methodology is proposed for modeling a large data set with a large number of parameters. The basic idea is to apply the maximum likelihood estimator to data observed at each time separately, and then combine these results via weighted averages so that the final estimator becomes the maximum likelihood estimator of the whole data set (full MLE). The asymptotic distribution and inference of the proposed estimators is derived. Simulation studies show that the proposed procedure gives exactly the same performance as the full MLE, but the proposed method is computationally feasible while the full MLE is not, and has much lower computational cost than the full MLE if both methods work. The proposed method is applied to estimate the number of drug-abusers in Hong Kong over the period 1977–2014.