المؤلفون: McGrath, Sean¹ (AUTHOR) sean_mcgrath@g.harvard.edu, Zhao, XiaoFei² (AUTHOR), Ozturk, Omer³ (AUTHOR), Katzenschlager, Stephan⁴ (AUTHOR), Steele, Russell⁵ (AUTHOR), Benedetti, Andrea^6,7,8 (AUTHOR)

المصدر: Research Synthesis Methods. Mar2024, Vol. 15 Issue 2, p332-346. 15p.

مصطلحات موضوعية: *MEDIAN (Mathematics), *RESEARCH personnel

مستخلص: When performing an aggregate data meta‐analysis of a continuous outcome, researchers often come across primary studies that report the sample median of the outcome. However, standard meta‐analytic methods typically cannot be directly applied in this setting. In recent years, there has been substantial development in statistical methods to incorporate primary studies reporting sample medians in meta‐analysis, yet there are currently no comprehensive software tools implementing these methods. In this paper, we present the metamedian R package, a freely available and open‐source software tool for meta‐analyzing primary studies that report sample medians. We summarize the main features of the software and illustrate its application through real data examples involving risk factors for a severe course of COVID‐19. [ABSTRACT FROM AUTHOR]

المؤلفون: HUSSAIN, SAJAD¹ sajad.stat321@gmail.com, BHAT, VILAYAT ALI¹ vilayat.stat@gmail.com

المصدر: Reliability: Theory & Applications. Mar2023, Vol. 18 Issue 1, p242-249. 8p.

مصطلحات موضوعية: *MEDIAN (Mathematics), *APPROXIMATION theory, *NUMERICAL analysis

مستخلص: The problem of biasness and availability of auxiliary variable for the estimating population mean is a big concern, both can be handled by proposing unbiased estimators in the absence of auxiliary variable. So in this paper unbiased exponential type estimators of population mean have been proposed. The estimators are proposed in the absence of the instrumental variable called the auxiliary variable by taking the advantage of the population and the sample median of the study variable. To about the first order approximation, the theoretical formulations of the bias and mean square error (MSE) are obtained. The circumstances in which the suggested estimators have the lowest mean squared error values when compared to the existing estimators were also deduced. In comparison to the currently used estimators, it was discovered that the suggested estimators of population mean had the lowest MSE, hence highest efficiency. Also least influence from the data's influential observations when it came to accurately calculating the population mean for skewed data. The theoretical findings of the paper are validated by the numerical study. [ABSTRACT FROM AUTHOR]

المؤلفون: McGrath, Sean¹ (AUTHOR) sean_mcgrath@g.harvard.edu, Katzenschlager, Stephan² (AUTHOR), Zimmer, Alexandra J^3,4 (AUTHOR), Seitel, Alexander⁵ (AUTHOR), Steele, Russell⁶ (AUTHOR), Benedetti, Andrea^3,7,8 (AUTHOR)

المصدر: Statistical Methods in Medical Research. Feb2023, Vol. 32 Issue 2, p373-388. 16p.

مصطلحات موضوعية: *MEDIAN (Mathematics), *STANDARD deviations, *SAMPLING errors, *MULTIPLE imputation (Statistics)

مستخلص: We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this article, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in poor coverage for the pooled mean in common effect meta-analyses and overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve the estimation of the within-study standard errors and consequently improve coverage for the pooled mean in common effect meta-analyses and estimation of between-study heterogeneity in random effects meta-analyses. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19. [ABSTRACT FROM AUTHOR]

المؤلفون: Boman, Mattias¹ (AUTHOR) mattias.boman@sta.uwi.edu

المصدر: Applied Economics. Nov2022, Vol. 54 Issue 55, p6393-6405. 13p. 4 Charts, 2 Graphs.

مصطلحات موضوعية: Willingness to pay, Contingent valuation, Valuation, Median (Mathematics), Low-income countries

مستخلص: This paper reviews the contingent valuation literature on hypothetical bias and valuation uncertainty, with special emphasis on measures of central tendency suitable for applied welfare analysis. In a theoretical scenario without valuation uncertainty, sample mean willingness to pay (WTP) is an estimator of population mean true WTP, the appropriate welfare measure. It is proposed here that this may not hold under valuation uncertainty. In this case, mean true WTP should be bounded by mean hypothetical WTP and mean actual WTP (in turn, mean actual WTP should exceed mean certain WTP). Based on a theoretical model and a review of existing empirical studies, median hypothetical WTP was found to be an estimator of mean true WTP. It is therefore proposed that contingent valuation researchers should consider using the sample hypothetical median as an estimator of population mean true WTP when supporting data on the degree of valuation uncertainty are absent. This could be a straightforward approach, e.g. in a low income country context, where the possibility of financing elaborate research designs accounting for valuation uncertainty is limited. It can also prove useful to revisit existing contingent valuation studies with these findings in mind. [ABSTRACT FROM AUTHOR]

المؤلفون: Kazunga, Cathrine, Bansilal, Sarah, Chiromo, Lytion

المصدر: African Journal of Research in Mathematics, Science & Technology Education; Dec2023, Vol. 27 Issue 3, p367-382, 16p

مصطلحات موضوعية: STUDENT teachers, STATISTICAL literacy, MEDIAN (Mathematics), PROBLEM solving, PRIMARY schools

مستخلص: The development of statistical literacy has become a key outcome of mathematics curricula in various countries. The purpose of the study was to explore primary pre-service teachers' (PSTs') knowledge of aspects of measures of central tendency, which is a central concept in statistical literacy. The 183 PSTs' written responses to four tasks were analysed in terms of demands elucidated by the Mathematical Knowledge for Teaching (MKT) framework. The results showed that almost all the participants were able to carry out simple computations of the mean and median and were generally able to identify learner errors. However, they found it much harder to solve problems that required unpacking of the procedures and comparison of different measures of central tendency. They also struggled with providing suitable feedback based on learner errors. This study shows that primary school PSTs need more support in developing these MKT skills with respect to the concepts of the mean and median. [ABSTRACT FROM AUTHOR]

: Copyright of African Journal of Research in Mathematics, Science & Technology Education is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: JIAN LIU¹ China99jian@163.com

المصدر: International Journal of Geometry. Jan2022, Vol. 11 Issue 1, p104-121. 18p.

مصطلحات موضوعية: *TRIANGLES, *MEDIAN (Mathematics)

مستخلص: Two new proofs of an acute triangle inequality involving medians and sides are obtained. Some applications of this inequality are also given. [ABSTRACT FROM AUTHOR]

المؤلفون: Kaftan, D. V.¹ (AUTHOR) blond.programmist@gmail.com

المصدر: Computational Mathematics & Modeling. Apr2021, Vol. 32 Issue 2, p253-257. 5p.

مصطلحات موضوعية: *MEDIAN (Mathematics)

مستخلص: We construct a checking test for a read-once alternative in a median-augmented element basis. We prove that the augmentation of the element basis with a median conserves the linearity of the Shannon function for the test length with respect to a read-once alternative. [ABSTRACT FROM AUTHOR]

المؤلفون: Zhang, Huishuai, Chi, Yuejie, Liang, Yingbin

المصدر: IEEE Transactions on Nuclear Science. Nov2018, Vol. 64 Issue 11, p7287-7310. 24p.

مصطلحات موضوعية: MEDIAN (Mathematics), HIGH-dimensional model representation, GAUSSIAN processes, X-ray crystallography, SIGNAL processing

مستخلص: This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a novel approach to robustify the gradient descent algorithm by using the sample median as a guide for pruning spurious samples in initialization and local search. Adopting a Poisson loss and a reshaped quadratic loss, respectively, we obtain two algorithms termed median-truncated Wirtinger flow and median-reshaped Wirtinger flow, both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

: Copyright of IEEE Transactions on Nuclear Science is the property of IEEE and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: Amiri, Mehdi¹ (AUTHOR), Jamalizadeh, Ahad^2,3 (AUTHOR) A.Jamalizadeh@uk.ac.ir

المصدر: Communications in Statistics: Theory & Methods. 2019, Vol. 48 Issue 13, p3413-3420. 8p.

مصطلحات موضوعية: *GAUSSIAN distribution, *STATISTICAL sampling, MEDIAN (Mathematics), STOCHASTIC orders

مستخلص: In this paper, we discuss some stochastic comparisons for the sample median in a random sample from a normal distribution. Specifically, we establish that the sample median is stochastically farther than the sample mean to the population mean. To verify the result of comparison, we derive an upper bound for some distributional characteristics of the distance between the sample median and the population mean. The stochastic ordering considered here is the likelihood ratio order. [ABSTRACT FROM AUTHOR]

: Copyright of Communications in Statistics: Theory & Methods is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

المؤلفون: BUCHIN, MAIKE, DRIEMEL, ANNE, ROHDE, DENNIS

المصدر: ACM Transactions on Algorithms; Jan2023, Vol. 19 Issue 1, p1-32, 32p

مصطلحات موضوعية: MEDIAN (Mathematics), SAMPLING (Process), APPROXIMATION algorithms, CURVES

مستخلص: In 2015, Driemel, Krivošija, and Sohler introduced the k,ℓ-median clustering problem for polygonal curves under the Fréchet distance. Given a set of input curves, the problem asks to find k median curves of at most ℓ vertices each that minimize the sum of Fréchet distances over all input curves to their closest median curve. A major shortcoming of their algorithm is that the input curves are restricted to lie on the real line. In this article, we present a randomized bicriteria-approximation algorithm that works for polygonal curves in ℝd and achieves approximation factor (1+ɛ) with respect to the clustering costs. The algorithm has worst-case running time linear in the number of curves, polynomial in the maximum number of vertices per curve (i.e., their complexity), and exponential in d, ℓ, 1/ɛ and 1/δ (i.e., the failure probability). We achieve this result through a shortcutting lemma, which guarantees the existence of a polygonal curve with similar cost as an optimal median curve of complexity ℓ, but of complexity at most 2ℓ -2, and whose vertices can be computed efficiently. We combine this lemma with the superset sampling technique by Kumar et al. to derive our clustering result. In doing so, we describe and analyze a generalization of the algorithm by Ackermann et al., which may be of independent interest. [ABSTRACT FROM AUTHOR]

: Copyright of ACM Transactions on Algorithms is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)