Nonparametric Estimation of Distribution Function using Bezier Curve

Bae, Whasoo; Kim, Ryeongah; Kim, Choongrak

doi:10.5351/csam.2014.21.1.105

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2016

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“…Kim et al (2000) applied Bezier curve smoothing to the estimation of the measurement error model. Further use of the Bezier curve are the smoothing of the KaplanMeier estimator (Kim et al, 2003), the smoothing of the bivariate Kaplan-Meier estimator (Bae et al, 2005), the selection of Bezier points in density estimation and regression (Kim and Park, 2012) and the nonparametric estimation of distribution function using the Bezier curve (Bae et al, 2014). Note that the kernel smoothing has a poor performance at the boundary, especially in the survival function estimation.…”

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confidence: 99%

Bezier curve smoothing of cumulative hazard function estimators

Cha

Kim

2016

CSAM

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In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

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