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- W4253852081 abstract "Publisher SummaryThis chapter discusses linear moment problems, such as those of minimizing and maximizing an expectation with statistical applications. Many such problems arise, especially in nonparametric theory, and require that a functional involving the distribution function be minimized or maximized when some of the moments of the distribution function are given, such as the mean and variance. An important problem is to find the distribution function having prescribed mean and variance for which the mean range of a random sample is minimized. Similar problems of optimization involving the extrema of the expected value of the largest or smallest order statistic occur in statistics. Two basic approaches are used in the optimization of moment integrals. One is the classical variational approach and the other is through the geometry of moment spaces. The chapter discusses the approach through the geometry of moments and studies several statistical applications. An important role in variational techniques is played by the Hahn–Banach theorem, and, for the sake of illustration, the chapter utilizes it to solve a moment problem." @default.
- W4253852081 created "2022-05-12" @default.
- W4253852081 date "1976-01-01" @default.
- W4253852081 modified "2023-09-27" @default.
- W4253852081 title "Chapter IV Linear Moment Problems" @default.
- W4253852081 doi "https://doi.org/10.1016/s0076-5392(08)60222-2" @default.
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