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- W2510082553 abstract "BY error analysis of a computation t on data d, we mean an assessment of the possible values of t which might be obtained for various hypothetical data d* similar to d. For example, if d is supposed generated by some probability model P, we might ask for the distribution of t(d*), where d* is randomly generated by P. We will be concerned with data d which are organized as a random sample xl, ..., XN from some population. Our error analysis will concentrate on the distribution of t(XN+l, ..., X2N), where XN+l, ..., X2N represents a further random sample of size N from the same population. An empirical error analysis may be performed by recomputing t for various replaced samples (RS), that is, samples of size n, obtained from xl, ..., XN by sampling with replacement. The problem is to relate these replaced sample values of t to the values of t which would be obtained in a future sample. We approach this problem by considering a very special computation-the mean of normal variables. In this case we show a relationship between certain RS values and future t values: these RS values are exchangeable, in distribution, with the variable t(XN+l, ..., X2N) given t(xl, ...XN). This very satisfying interpretation requires a Bayesian argument with uniform prior on the population mean. A non-Bayesian interpretation is also available for these RS values; the set of RS values is a typical set for t, that is the gaps between the ordered RS values contain t with equal probability. These interpretations add nothing to the error analysis of a normal mean, but, because empirical error analysis may be performed under very general conditions (we need only that d may be regarded as a random sample of size N, and that t be defined for all samples of size N), the connection between empirical error and future error derived in the normal case is potentially very useful. We need to know how well this connection holds up under non-normal conditions. Asymptotic arguments are available to establish the two interpretations, as holding asymptotically, in a wide range of situations. Experimental investigation is necessary to test the validity of the interpretations in problems of frequent interest. Eigenvector analysis is considered here." @default.
- W2510082553 created "2016-09-16" @default.
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- W2510082553 date "1971-01-01" @default.
- W2510082553 modified "2023-09-23" @default.
- W2510082553 title "Error Analysis by Replaced Samples" @default.
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- W2510082553 doi "https://doi.org/10.1111/j.2517-6161.1971.tb00861.x" @default.
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