A semiparametric estimator of the distribution function of a variable measured with error |
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Authors: | Cong Chen Wayne A. Fuller F. Jay Breidt |
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Affiliation: | Merck Research Labs, Merck k Co., Inc , West Point, PA, 19488 |
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Abstract: | The estimation of the distribution functon of a random variable X measured with error is studied. Let the i-th observation on X be denoted by YiXi+εi where εi is the measuremen error. Let {Yi} (i=1,2,…,n) be a sample of independent observations. It is assumed that {Xi} and {∈i} are mutually independent and each is identically distributed. As is standard in the literature for this problem, the distribution of e is assumed known in the development of the methodology. In practice, the measurement error distribution is estimated from replicate observations. The proposed semiparametric estimator is derived by estimating the quantises of X on a set of n transformed V-values and smoothing the estimated quantiles using a spline function. The number of parameters of the spline function is determined by the data with a simple criterion, such as AIC. In a simulation study, the semiparametric estimator dominates an optimal kernel estimator and a normal mixture estimator for a wide class of densities. The proposed estimator is applied to estimate the distribution function of the mean pH value in a field plot. The density function of the measurement error is estimated from repeated measurements of the pH values in a plot, and is treated as known for the estimation of the distribution function of the mean pH value. |
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Keywords: | Cubic spline Normal transformation Post-stratification Preci¬sion farming Weight estimation |
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