JournalISSN: 0003-4851

Annals of Mathematical Statistics

Institute of Mathematical Statistics
About: Annals of Mathematical Statistics is an academic journal. The journal publishes majorly in the area(s): Population & Section (fiber bundle). It has an ISSN identifier of 0003-4851. It is also open access. Over the lifetime, 3885 publications have been published receiving 337347 citations. The journal is also known as: Ann. Math. Stat. & The Annals of mathematical statistics.

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14,407 citations

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TL;DR: In this paper, the authors show that the limit distribution is normal if n, n\$ go to infinity in any arbitrary manner, where n = m = 8 and n = n = 8.
Abstract: Let \$x\$ and \$y\$ be two random variables with continuous cumulative distribution functions \$f\$ and \$g\$. A statistic \$U\$ depending on the relative ranks of the \$x\$'s and \$y\$'s is proposed for testing the hypothesis \$f = g\$. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis \$f = g\$ the probability of obtaining a given \$U\$ in a sample of \$n x's\$ and \$m y's\$ is the solution of a certain recurrence relation involving \$n\$ and \$m\$. Using this recurrence relation tables have been computed giving the probability of \$U\$ for samples up to \$n = m = 8\$. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if \$m, n\$ go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives \$f(x) > g(x)\$ for every \$x\$.

9,469 citations

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TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Abstract: : Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and of determining the mode of a probability function are discussed. Only estimates which are consistent and asymptotically normal are constructed. (Author)

9,261 citations

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TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Abstract: Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where a is a given constant. We give a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability.

7,621 citations

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TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.
Abstract: This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)

5,129 citations

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No. of papers from the Journal in previous years
YearPapers
19731
1972223
1971228
1970227
1969218
1968223