5 research outputs found
Smoothed Empirical Likelihood Methods for Censored Quantile Regression
ํ์๋
ผ๋ฌธ (์์ฌ)-- ์์ธ๋ํ๊ต ๋ํ์ : ๊ฒฝ์ ํ๋ถ, 2013. 8. ํฉ์ค์ฌ.๋ณธ ๋
ผ๋ฌธ์์๋ ์ค๋์ ๋จํ๊ท๋ชจํ์ ๋ชจ์ ์ถ์ ์ ์ํ ๊ฒฝํ์ ์ฐ๋ ๋ฐฉ๋ฒ(Whang, 2003)์ ์ ์ฉ์ฑ์ ์๋ฎฌ๋ ์ด์
์ ํตํ์ฌ ๊ฒ์ฆํด ๋ณด์๋ค. ์ฐ๋ฆฌ๋ ๊ณ ์ฐจ ์ ์ ๋ฅผ ์ํ์ฌ ๋น๋ชจ์ ์ปค๋ ํจ์๋ฅผ ์ด์ฉํ์ฌ ์ค๋์ ๋จํ๊ท๋ชจํ ์ถ์ ํจ์๋ฅผ ํํํํ์๋ค. ๋ณธ ์ฐ๊ตฌ์์๋ ์ค๋์ ๋จํ๊ท ์ถ์ ๋๊ณผ ์ผ์ฐจ ๋๋ฑํ๋ค๊ณ ์๋ ค์ง ํํํ๋ ๊ฒฝํ์ ์ฐ๋ ์ถ์ ๋์ผ๋ก ๊ตฌํ ์ ๋ขฐ ๊ตฌ๊ฐ์ด ํฌํจ์ค์ฐจ ์ฐจ์ O(n^(-1))๋ฅผ ๊ฐ์ง์ ๋ณด์๋ค. ๋ชฌํ
์นด๋ฅผ๋ก ์คํ์ ๋ฐํ๋ ๋ณด์ ๋ ํํํ๋ ๊ฒฝํ์ ์ฐ๋ ๋ฐฉ๋ฒ์ด ์์ ํ๋ณธ์์ ์ข์ ํ์์ผ๋ฉฐ, ์ผ๋ฐ์ ์ผ๋ก ์ฌ์ฉ๋๋ ๋ถํธ์คํธ๋ฉ ๋ฐฉ๋ฒ๋ณด๋ค ๋ ์ ํํ ๊ฒฐ๊ณผ๋ฅผ ๋์ถํจ์ ๋ํ๋ธ๋ค. ๋ํ, ์๋ฎฌ๋ ์ด์
๊ฒฐ๊ณผ๋ ํํํ๋ ๊ฒฝํ์ ์ฐ๋ ๋ฐฉ๋ฒ์ด ๋นํํํ๋ ๊ฒฝํ์ ์ฐ๋ ๋ฐฉ๋ฒ๋ณด๋ค ๋ ๋์ ๊ฒฐ๊ณผ๋ฅผ ๋์ถํ๋ค๋ ๊ฒ์ ํ์ธํ์๋ค. ์ด๋ ๋ฐํ๋ ๋ณด์ ์ด ํํํ๋ ๊ฒฝํ์ ์ฐ๋ ๋ฐฉ๋ฒ ์ ๋ขฐ ๊ตฌ๊ฐ์ ํฌํจ ์ค์ฐจ ์ฐจ์๋ฅผ O(n^(-2))๋ก ์ค์ธ๋ค๋ Whang (2003)์ ์ด๋ก ๊ณผ ๋ถํฉํ๋ ๊ฒฐ๊ณผ๋ฅผ ๋ณด์ฌ์ค๋ค.This article verifies the efficiency of the empirical likelihood method to estimate the parameters of the censored quantile regression models suggested by Whang (2003) via simulation. We smooth the simple estimating equation in a censored quantile regression model with a nonparametric kernel function for higher order refinements. We show that the confidence region based on the smoothed empirical likelihood estimator, known to be the first-order equivalent to the standard censored quantile estimator, has coverage error of order O(n^-1). Monte Carlo experiments suggest that the Bartlett corrected smoothed empirical likelihood method performs well in small samples, and it provides more accurate and computationally efficient results than the commonly used (smoothed) bootstrap methods. Moreover, simulation results show that the proposed confidence region has better finite sample performance than the confidence interval obtained from the un-corrected smoothed empirical likelihood estimation, which are consistent with the argument of Whang (2003) that Bartlett correction can reduce the coverage error of smoothed empirical likelihood confidence region to order O(n^-2).Maste