Annals 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 publication(s) have been published receiving 337347 citation(s). The journal is also known as: Ann. Math. Stat. & The Annals of mathematical statistics.
Topics: Population, Section (fiber bundle), Asymptotic distribution, Random variable, Multivariate normal distribution
Papers published on a yearly basis
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 $x$.
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)
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.
Peter J. Huber1•Institutions (1)
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.)
Related Journals (5)
Journal of the American Statistical Association
13.4K papers, 1.6M citations
Journal of the royal statistical society series b-methodological
1.8K papers, 414.3K citations
7K papers, 732.2K citations
Annals of Statistics
5.6K papers, 601.9K citations
4.9K papers, 600.6K citations