DOI QR코드

DOI QR Code

Derivation and verification of influence function on parameter δ proposed by Ghosh and Kim

Ghosh와 Kim 모수 δ의 영향함수 유도 및 확인

  • Kim, Minjeong (Income Statistics Division, Statistics Korea) ;
  • Kim, Honggie (Department of Information and Statistics, Chungnam National University)
  • Received : 2017.04.10
  • Accepted : 2017.07.27
  • Published : 2017.08.31

Abstract

The Ghosh and Kim zero-altered distribution model is used to analyze count data that have too many or too few zeros. The dispersion type parameter ${\delta}$ in the zero-altered distribution model consists of mean, variance and zero probability and has two forms depending on the relation between ${\mu}$ and ${\sigma}^2$. We derived the influence function on ${\delta}$ when ${\sigma}^2{\geq}{\mu}$. To show the validity of the influence function, we used the Census data on the number of births of married women in Korea to compare the estimated changes in ${\delta}$ using this function with those obtained using the direct deletion method. The result proved that the obtained influence function is very accurate in estimating changes in ${\delta}$ when an observation is deleted.

Ghosh와 Kim에 의해 소개된 영 변환 모형은 0이 많거나 적을 때 계수형 자료(count data)를 분석하는 모형이다. 이 모형의 산포형태모수는 평균과 분산, 0 확률로 구성되며 ${\mu}$${\sigma}^2$의 관계에 따라 2가지 형태를 가진다. 본 논문에서는 ${\sigma}^2{\geq}{\mu}$일 때, Ghosh와 Kim 영 변환확률 모형의 모수 ${\delta}$에 대한 영향함수를 도출하였다. 도출한 영향함수의 타당성을 검증하기 위해서 인구주택총조사 자료를 이용해 관측치가 제거된 경우에서 영향함수로 도출한 ${\delta}$ 추정치 변화값과 직접 계산한 ${\delta}$ 추정치 변화값을 비교하였다. 그 결과 영향함수는 ${\delta}$의 변화를 매우 정확히 추정하였다.

Keywords

References

  1. Campbell, N. A. (1978). The in uence function as and aid in outlier detection in discrimination analysis, Applied Statistics, 27, 251-258. https://doi.org/10.2307/2347160
  2. Cook, R. D. and Weisberg, S. (1980). Characterization of and empirical in uence function for detecting in uential cases in regression, Technometrics, 22, 495-508. https://doi.org/10.1080/00401706.1980.10486199
  3. Cook, R. D. and Weisberg, S. (1982). Residual and Influence in Regression, Chapman and Hall, New York.
  4. Critchley, F. (1985). In uence in principal components analysis, Biometrika, 72, 627-626. https://doi.org/10.1093/biomet/72.3.627
  5. Ghosh, S. K. and Kim, H. (2007). Semiparametric inference based on a class of zero-altered distributions, Statistical Methodology, 4, 371-383. https://doi.org/10.1016/j.stamet.2007.01.001
  6. Hampel, F. (1974). The in uence curve and its role in robust estimation, Journal of American Statistical Association, 69, 383-393. https://doi.org/10.1080/01621459.1974.10482962
  7. Kim, H. (1992). Measures of in uence in correspondence analysis, Journal of Statistical Computation and Simulation, 40, 201-207. https://doi.org/10.1080/00949659208811377
  8. Kim, H. (1994). In uence functions in multiple correspondence analysis, The Korean Journal of Applied Statistics, 7, 69-74.
  9. Kim, H. (1998). A study on cell in uences to ${\chi}^2$ statistics in contingency tables, The Korean Communications in Statistics, 5, 35-42.
  10. Kim, H. and Lee, H. (1996). In uence function on ${\chi}^2$ statistics in contingency tables, The Korean Communications in Statistics, 7, 69-76.
  11. Kim, H., Lee, Y., Shin, H., and Lee, S. (2003). In uence function on tolerance limit, The Korean Communications in Statistics, 10, 497-505.
  12. Kim, H., Ra, Y., Kim, K., and Lee, Y. (2013). Analysis of the trend of the number of children of married women in Korea using zero-altered distribution, Journal of Korean Official Statistics, 18, 1-15.
  13. Kim, K. (2005). The in uence function in t statistic and the test of its validity (master's thesis), Chungnam National University, Daejeon.
  14. Radhakrishnan, R. and Kshirsagar, A. M. (1981). In uence functions for certain parameters in multi-variate analysis, Communication in Statistics A, 10, 515-529. https://doi.org/10.1080/03610928108828055