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Influence Curves for Randomly Truncated Data

Min-Te Chao
Biometrika
Vol. 74, No. 2 (Jun., 1987), pp. 426-429
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336158
Stable URL: http://www.jstor.org/stable/2336158
Page Count: 4
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Influence Curves for Randomly Truncated Data
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Abstract

Under a random truncation model, observations (X, Y) are lost if $X < Y$. Properties of the maximum likelihood estimators for the distributions F, G of X and Y and the truncation proportion α have been treated by various authors, for example, Lynden-Bell (1971), and more recently Woodroofe (1985). Asymptotic variances of various estimates, including the mean, the median, the L- and the M-estimates and $\hat\alpha$, if they can be expressed as functionals of F̂ and Ĝ, are obtained through the concept of influence curves. The asymptotic variance of α̂ is derived to illustrate our method.

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