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\noindent Statistica Sinica {\bf 13}(2003), 275-282
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\centerline{\large\bf STRONG GAUSSIAN APPROXIMATIONS IN THE}
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\centerline{\large\bf LEFT TRUNCATED AND RIGHT CENSORED MODEL}
\vspace{.25cm}
\centerline{SzeMan Tse}
\vspace{.4cm}
\centerline{\it National Donghua University}
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\begin{quotation}
\noindent {\it Abstract:}
In this paper, we consider the Tsai-Jewel-Wang estimator
$F^0_n(x)$ of an unknown distribution function $F^0$ when the data are
subject to random left truncation and right censorship. Strong Gaussian
approximations of the product-limit process $\sqrt n [F_n^0(x)-F^0(x)]$
are constructed with rate $O({(\log n)^{3/2}/n^{1/8}})$. A functional
law of the iterated logarithm for the maximal deviation of the estimator
from the estimand is derived from the construction.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Cumulative hazard, left truncation, Gaussian approximations,
right censorship, product-limit.\par
\end{quotation}
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