Sequential Statistics
Designed for students with familiarity in advanced calculus, probability and statistical inference, this text provides only elementary proofs, and maintains mathematics and statistics at a basic level.
TABLE OF CONTENTS Sequential Statistics
4.10: Nonparametric Confidence Intervals
4.10 Nonparametric Confidence Intervals
4.10.1 Confidence Intervals for the p-point of a Distribution Function
Farrell (1966a, 1966b) has given two sequential procedures for setting up bounded width confidence intervals for'the p-point of a distribution function that are based on the i.i.d. sequence of random variables { X n, n>1}. For further details, the reader is referred to Govindarajulu (1987, Section 5.11.1).
4.10.2 Confidence Intervals for Other Population Parameters
Geerstsema (1970a) has applied the methods of Section 4.7 for constructing a sequential nonparametric confidence interval procedure for certain population parameters. Notice that the methods of Section 4.6 will not apply here since the functional form of the density is unknown.
A General Method for Constructing Bounded Length Confidence Intervals
Let X 1, X 2,..., X n be a fixed random sample of size n from a population having F for its cumulative distribution function (cdf) and let ? be a parameter of the population. We are interested in constructing for ?, a confidence interval of length not larger than 2 d. For each positive integer n, consider two statistics L n and U n (not depending on d) based on the first n observations, such that L n< U n a.s. and lim n ?? P(L n ? ? ?U n )=1 ? ? (so that, for n large, (L n ,U n ) is a confidence...
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