Smoothing signals for semimartingales
The kernel function and convolution-smoothing methods developed to estimate a probability density function and distribution are essentially a way of smoothing the empirical distribution function. This paper shows now one can generalize these methods to estimate signals for a semimartingale model. A convolution-smoothed estimate is used to obtain an absolutely continuous estimate for an absolutely continuous signal of a semimartingale model. This provides a method of obtaining a convolution-smoothed estimate of the cumulative hazard function in the censored case, an open problem proposed by Mack (Bulletin of Informatics and Cybernetics 21 (1984) 29-35). Asymptotic properties of the convolution-smoothed estimate are discussed in some detail.
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Volume (Year): 28 (1988)
Issue (Month): 1 (April)
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