臺灣博碩士論文加值系統

本文中，依據Hollander和Pe na’s(1992)對於設限資料所提出的適合度檢定，我們推導截取資料下的模式適合度檢定。檢定統計量為Wald型式且在虛擬假設下其漸近分配為卡方分配。模擬結果顯示在截取比例不大的情況下，該檢定可以達到正確的顯著水準。

In this article, procedures analogous to Hollander and Pe˜na’s goodness-of-fit test for censored data are developed under random truncation model. This leads to the development of an asymptotic test based on a Wald-type statistic with a chi-squared limiting null distribution. The general conclusions from the simulation study are that the proposed test usually achieves the desired signifcance levels when the probability
of truncation is not too large.

ABSTRACT............................................2
摘要................................................3
第一章 簡介........................................4
第二章 檢定方法....................................7
定理 2.1..........................................8
定理 2.2..........................................9
定理 2.3..........................................10
定理 2.4..........................................11
第三章 模擬結果....................................13
參考文獻............................................16

Akritas, M. G. (1988) Pearson-type goodness-of-fit test: The univariate case. JASA, 83, 222-230.
Billingsley, P. (1968)., Convergence of probability measure, New York: John Wiley.
Guilbaud, O. (1988). Exact Kolmogorov-type tests for left-truncated and /or right-censored data. J. Am. Statist. Ass. 83, 2130-221.
Habib, M. G. and Thomas, D. R. (1986) Chi-square goodness-of-fit tests for randomly censored data. Ann. Statist. 14, 759-765.
He, S. and Yang, G. L. (1998). The strong law under random truncation. Ann. Statist. 26, 992-1010.
Hollander, M. and Pe˜na, E. A. (1992). A chi-squared goodness-of-fit test for randomly censored data. J. Am. Statist. Ass. 87, 458-463.
Hwang, Y-T and Lin, J.-S. (2003). Goodness of fit tests for randomly truncated data (submitted).
Hyde, J. (1977) Testing survival under right censoring and left truncation Biometrika 64, 225-230.
Keiding, N., and Gill, R. (1990). Random truncation models and Markov Process. Ann. Statist. 18, 582-602.
Lynden-Bell, D. (1971). A method of allowing for known observational selection in small samples applied to 3CR quasars. Mon. Not. R. Astr. Soc. 155, 95-118.
Moore, D. (1978). Chi-squared test, in Studies in Statistics ed. R. V. Hogg, Washington DC: Mathmatical Association of America, pp 66-106.
Vardi, Y. (1985). Empirical distribution in selection bias models. Ann. Statist. 10, 616-621.
Wang, M.-C., Jewell, N. P. and Tsai, W.-Y. (1986). Asymptotic properties of the product-limit estimate under random truncation. Ann. Statist. 14, 1597-1605.
Wang, M.-C. (1989). A semiparametric model for randomly truncated data. J. Am. Statist. Ass. 84, 742-748.
Wang, M.-C. (1991). Nonparametric estimation from cross-sectional survival data. J. Am. Statist. Ass. 86, 130-143.
Woodroofe, M. (1985). Estimating a distribution function with truncated data. Ann. Statist. 13, 163-167.