scispace - formally typeset
Search or ask a question

Showing papers in "Annals of Mathematical Statistics in 1945"


Book ChapterDOI
Abraham Wald1
TL;DR: A sequential test of a statistical hypothesis is defined as any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation.
Abstract: By a sequential test of a statistical hypothesis is meant any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation. Thus, such a test procedure is carried out sequentially. On the basis of the first trial, one of the three decisions mentioned above is made. If the first or the second decision is made, the process is terminated. If the third decision is made, a second trial is performed. Again on the basis of the first two trials one of the three decisions is made and if the third decision is reached a third trial is performed, etc. This process is continued until either the first or the second decision is made.

1,463 citations



Journal ArticleDOI
TL;DR: In this paper, the authors validate the existing solutions of (i) and (ii) assuming only a continuous probability density, and then modifies these solutions so that they are valid for any $cdf$ whatever.
Abstract: Previous work on non-parametric estimation has concerned three problems: (i) confidence intervals for an unknown quantile, (ii) population tolerance limits, (iii) confidence bands of an unknown cumulative distribution function $(cdf)$. For problem (iii) a solution has been available which is valid for any $cdf$ whatever, but for (i) and (ii) it has heretofore assumed that the population has continuous probability density. This paper validates the existing solutions of (i) and (ii) assuming only a continuous $cdf$. It then modifies these solutions so that they are valid for any $cdf$ whatever.

105 citations



Book ChapterDOI
TL;DR: The problem of estimating the error in the normal approximation to the binominal distribution has been studied extensively in the literature as mentioned in this paper, but not all pertinent questions have found a satisfactory solution.
Abstract: Although the problem of an efficient estimation of the error in the normal approximation to the binominal distribution is classical, the many papers which are still being written on the subject show that not all pertinent questions have found a satisfactory solution.

82 citations




Book ChapterDOI
TL;DR: In this article, a sequence of independent random variables with the same cumulative distribution function (V(x) is defined as a fair game, and the cumulative distribution is used to define the game.
Abstract: “Fair” games. Let \(\{X_k\}\) be a sequence of independent random variables with the same cumulative distribution function \(V(x)\).

57 citations























Journal ArticleDOI
TL;DR: In this paper, an estimate of the number of electoral votes that will be cast for a presidential candidate based on a poll of interviews in the ith state (i = 1, ^, 48) where the Xi are fixed constants > 0 such that 2Xi = 1 and the respondent is asked for which candidate he intends to cast his vote.
Abstract: To a.rrive at an estimate of the number of electoral votes that will be cast for a presidential candidate a poll is taken of XiN interviews in the ith state (i = 1, ^, 48) where the Xi are fixed constants > 0 such that 2Xi = 1 and the respondent is asked for which candidate he intends to cast his vote. To estimate the number of electoral votes wvhich candidate A will receive, the electoral votes of all the states in which the poll shows a majority for candidate A are added and their sum is used as an estimate for the number of electoral votes which candidate A will receive. In this paper certain properties of this estimate will be discussed. It will be showvn that it is a biased but consistent estimate and an upper bound for the bias vill be derived. Finally we shall derive that distribution of interviews which minimizes the variance of our estimate. In all that follows we shall consider the poll as a random or stratified random sample and shall disregard the bias introduced by inaccurate answers. Our results however remain valid as long as the sampling variance is proportional 1 to .