Topic
Arithmetic mean
About: Arithmetic mean is a research topic. Over the lifetime, 1450 publications have been published within this topic receiving 26372 citations. The topic is also known as: mean & average.
Papers published on a yearly basis
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Papers
TL;DR: In this article, the authors extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence, and they show that consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \ rightarrow 0$.
Abstract: We extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence. We do not attempt a reduction to i.i.d. values. The jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of $l$ consecutive data once. In the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero. Under appropriate conditions consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \rightarrow 0$. General statistics are approximated by an arithmetic mean. In regular cases this approximation determines the asymptotic behavior. Bootstrap replicates are constructed by selecting blocks of length $l$ randomly with replacement among the blocks of observations. The procedures are illustrated by using the sunspot numbers and some simulated data.
2,519 citations
TL;DR: The authors measured the mean, standard deviation, alpha, and beta of venture capital investments, using a maximum likelihood estimate that corrects for selection bias, and found that the bias-corrected estimation neatly accounts for log returns.
934 citations
TL;DR: This paper introduces metric-based means for the space of positive-definite matrices and discusses some invariance properties of the Riemannian mean, and uses differential geometric tools to give a characterization of this mean.
Abstract: In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization of this mean.
835 citations
TL;DR: If a population is growing in a randomly varying environment, such that the finite rate of increase per generation is a random variable with no serial autocorrelation, the logarithm of population size at any time t is normally distributed.
Abstract: If a population is growing in a randomly varying environment, such that the finite rate of increase per generation is a random variable with no serial autocorrelation, the logarithm of population size at any time t is normally distributed. Even though the expectation of population size may grow infinitely large with time, the probability of extinction may approach unity, owing to the difference between the geometric and arithmetic mean growth rates.
743 citations
TL;DR: It is shown how the non-parametric bootstrap provides a more flexible alternative for comparing arithmetic mean costs between randomized groups, avoiding the assumptions which limit other methods.
Abstract: Health economic evaluations are now more commonly being included in pragmatic randomized trials. However a variety of methods are being used for the presentation and analysis of the resulting cost data, and in many cases the approaches taken are inappropriate. In order to inform health care policy decisions, analysis needs to focus on arithmetic mean costs, since these will reflect the total cost of treating all patients with the disease. Thus, despite the often highly skewed distribution of cost data, standard non-parametric methods or use of normalizing transformations are not appropriate. Although standard parametric methods of comparing arithmetic means may be robust to non-normality for some data sets, this is not guaranteed. While the randomization test can be used to overcome assumptions of normality, its use for comparing means is still restricted by the need for similarly shaped distributions in the two groups. In this paper we show how the non-parametric bootstrap provides a more flexible alternative for comparing arithmetic mean costs between randomized groups, avoiding the assumptions which limit other methods. Details of several bootstrap methods for hypothesis tests and confidence intervals are described and applied to cost data from two randomized trials. The preferred bootstrap approaches are the bootstrap-t or variance stabilized bootstrap-t and the bias corrected and accelerated percentile methods. We conclude that such bootstrap techniques can be recommended either as a check on the robustness of standard parametric methods, or to provide the primary statistical analysis when making inferences about arithmetic means for moderately sized samples of highly skewed data such as costs.
730 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 4 |
| 2021 | 32 |
| 2020 | 63 |
| 2019 | 52 |
| 2018 | 38 |
| 2017 | 48 |