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Interval prediction on the sum of binary random variables indexed by a graph
Communications for Statistical Applications and Methods 2019;26:261-272
Published online May 31, 2019
© 2019 Korean Statistical Society.

Seongoh Parka, Kyu S. Hahnb, Johan Lima, Won Son1,c

aDepartment of Statistics, Seoul National University, Korea;
bDepartment of Communication, Seoul National University, Korea;
cThe Bank of Korea, Korea
Correspondence to: 1Economist, The Bank of Korea, 67, Sejong-daero, Jung-gu, Seoul 04514, Korea.
E-mail: son.won@gmail.com
Received October 15, 2018; Revised March 7, 2019; Accepted March 28, 2019.
 Abstract
In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the 19th and 20th Korea National Assembly elections.
Keywords : binary sum, exit poll, graph indexed variables, Korea National Assembly election, prediction interval, residual bootstrap, spatial auto-regressive model