American Journal of Applied Mathematics and Statistics
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American Journal of Applied Mathematics and Statistics. 2014, 2(6), 416-422
DOI: 10.12691/ajams-2-6-10
Open AccessArticle

Deconvolving Kernel Density Estimation of Right Censored Duration Data with Recall Errors

T. K. Chakrabarty1,

1Department of Statistics, North Eastern Hill University, Shillong, India

Pub. Date: December 30, 2014

Cite this paper:
T. K. Chakrabarty. Deconvolving Kernel Density Estimation of Right Censored Duration Data with Recall Errors. American Journal of Applied Mathematics and Statistics. 2014; 2(6):416-422. doi: 10.12691/ajams-2-6-10

Abstract

Demographic and Health Surveys (DHS) collect information on several landmark events retrospectively from the life or birth histories and recollections of past events of individuals. Retrospective information of the sort is known to be affected by recall errors which result in the misplacement of dates, and the distortion of reports of duration. For example, the retrospectively reported ages of weaning for all births that occurred during the three or five years preceding the survey are right censored and commonly display marked heaping at durations 12, 18 and 24 months. The present article at first tries to understand whether the heaping is a result of true behavior and societal norms or it is an age dependent outcome. Further, under an additive error model, a kernel-type deconvolving density estimator of weaning time is proposed by smoothing the increments of Kaplan-Meier (KM) cumulative distribution function. Using simulated data it has been shown that in small and moderately censored samples these estimators can reduce the bias substantially. Finally, an empirical illustration is provided using National Family Health Survey (NFHS-3, 2005-06) data from India.

Keywords:
weaning duration survival distribution kernel density smoothing deconvolution

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