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- W2090760933 abstract "The substitution procedure in the normal case, like using to mimici N(μ, σ 2), has been widely used in many branches of statistics, for examples, in the parametric bootstrap, in ranking and selection, in Kolmogorov-Smirnov test and many many practical situations. In view of these, a question has to be addressed “How big differences it may make with some certainty by using instead of N(μ, σ 2) ?” In this paper, we study this question by investigating asymptotics of the Kolmogorov type statistical functions, like . Three cases are considered here: (1) a normal distribution with its mean unknown and its variance known; (2) a normal distribution with its mean known and its variance unknown; (3) a normal distribution with its mean and variance unknown. We answered the preceding question in the sense of constructing asymptotic bands for normal distributions in these three cases. For the first two, the corresponding Kolmogorov type statistical functions follow folded normal distributions approximately. For the last one, the corresponding Kolmogorov type statistical function is stochastically less than or equal to a random variable with its distribution known." @default.
- W2090760933 created "2016-06-24" @default.
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- W2090760933 date "1995-01-01" @default.
- W2090760933 modified "2023-09-27" @default.
- W2090760933 title "Asymptotic confidence bands for normal distributions" @default.
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- W2090760933 doi "https://doi.org/10.1080/03610929508831513" @default.
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