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- W154507002 abstract "We first consider the deconvolution problem in a model with non-negative random variables and disturbances with a decreasing density. Formally, let Z1,..., Z n be a sample from a distribution function H with density $$h(z) = int {g(z - x)d{F_0}(x),z in R} $$ (2.1) where g is a decreasing density on [0, ∞), and F0 an unknown distribution function, concentrated on [0, ∞). For example, g could be the exponential density $$g(x) = {e^{ - x}}{1_{[0,infty )}}(x),x in R$$ or the Uniform (0,1) density $$g(x) = {1_{[0,1)}}(x),x in R$$ An NPMLE of F0 is a distribution function, maximizing $$psi (F) = int {log left{ {int g (z - x)dF(x)} right}d{H_n}(z)} $$ (2.2) as a function of F, where H n is the empirical distribution function of the sample Z1,..., Z n .KeywordsEmpirical Distribution FunctionIsotonic RegressionExponential DensityLeft DerivativeDeconvolution ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W154507002 date "1992-01-01" @default.
- W154507002 modified "2023-09-23" @default.
- W154507002 title "The Deconvolution Problem" @default.
- W154507002 doi "https://doi.org/10.1007/978-3-0348-8621-5_5" @default.
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