The American Statistician最新文献_第4页

Here Comes the STRAIN: Analyzing Defensive Pass Rush in American Football with Player Tracking Data 压力来了:用球员跟踪数据分析美式足球中的防守传球

The American Statistician Pub Date : 2023-05-17 DOI: 10.1080/00031305.2023.2242442

Quang Nguyen, Ronald Yurko, Gregory J. Matthews

{"title":"Here Comes the STRAIN: Analyzing Defensive Pass Rush in American Football with Player Tracking Data","authors":"Quang Nguyen, Ronald Yurko, Gregory J. Matthews","doi":"10.1080/00031305.2023.2242442","DOIUrl":"https://doi.org/10.1080/00031305.2023.2242442","url":null,"abstract":"In American football, a pass rush is an attempt by the defensive team to disrupt the offense and prevent the quarterback (QB) from completing a pass. Existing metrics for assessing pass rush performance are either discrete-time quantities or based on subjective judgment. Using player tracking data, we propose STRAIN, a novel metric for evaluating pass rushers in the National Football League (NFL) at the continuous-time within-play level. Inspired by the concept of strain rate in materials science, STRAIN is a simple and interpretable means for measuring defensive pressure in football. It is a directly-observed statistic as a function of two features: the distance between the pass rusher and QB, and the rate at which this distance is being reduced. Our metric possesses great predictability of pressure and stability over time. We also fit a multilevel model for STRAIN to understand the defensive pressure contribution of every pass rusher at the play-level. We apply our approach to NFL data and present results for the first eight weeks of the 2021 regular season. In particular, we provide comparisons of STRAIN for different defensive positions and play outcomes, and rankings of the NFL's best pass rushers according to our metric.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129050616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Response to Comment by Schilling 席林对评论的回应

The American Statistician Pub Date : 2023-04-20 DOI: 10.1080/00031305.2023.2205455

J. Bartroff, G. Lorden, Lijia Wang

{"title":"Response to Comment by Schilling","authors":"J. Bartroff, G. Lorden, Lijia Wang","doi":"10.1080/00031305.2023.2205455","DOIUrl":"https://doi.org/10.1080/00031305.2023.2205455","url":null,"abstract":"We appreciate the recent paper of Schilling and Stanley (2022, hereafter SS) on confidence intervals for the hypergeometric being brought to our attention, which we were not aware of while preparing our paper (Bartroff, Lorden, and Wang 2022, hereafter BLW) on that subject. Although there are commonalities between the two approaches, there are some important distinctions that we highlight here. Following those papers’ notations, below we denote the confidence intervals for the hypergeometric success parameter based on sample size n and population size N by LCO for SS, and C∗ for BLW. In the numerical examples below, LCO (github.com/mfschilling/ HGCIs) and C∗ (github.com/bartroff792/hyper) were computed using the respective authors’ publicly available R code, running on the same computer. Computational time. LCO and C∗ differ drastically in the amount of time required to compute them. Figure 1 shows the computational time of LCO and C∗ for α = 0.05, N = 200, 400, . . . , 1000, and n = N/2. For example, for N = 1000 the computational time of LCO exceeds 100 min whereas C∗ requires roughly 1/10th of a second (0.002 min). In further numerical comparisons not included here, we found this relationship to be common for moderate to large values of the sample and population sizes, n and N. This may be due to the algorithm for computing LCO which calls for searching among all acceptance functions of minimal span (SS, p. 37). Provable optimality. SS contains two proofs, one in the Appendix of a basic result about the hypergeometric parameters, and one in the main text of the paper’s only theorem (SS, p. 33) which is a general result that size-optimal hypergeometric acceptance sets are inverted to yield size-optimal confidence “intervals.” However, not all inverted acceptance sets will yield proper intervals, and in practice one often ends up with noninterval confidence sets, for example, intervals with “gaps.” This occurs when the endpoint sequences of the acceptance intervals being inverted are non-monotonic, or themselves have gaps. SS address this by modifying their proposal in this situation to mimic a method of Schilling and Doi (2014) developed for the Binomial distribution. SS (pp. 36–37) write, Where there is a need to resolve a gap, in which case the minimal span acceptance function that causes the gap is replaced with the one having the","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117097802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hierarchical Spatio-Temporal Change-Point Detection 分层时空变化点检测

The American Statistician Pub Date : 2023-04-11 DOI: 10.1080/00031305.2023.2191670

引用次数: 4

Comment on “A Case for Nonparametrics” by Bower et al. 对Bower等人的“非参数的一种情况”的评论。

The American Statistician Pub Date : 2023-04-03 DOI: 10.1080/00031305.2023.2172078

K. Rice, T. Lumley

{"title":"Comment on “A Case for Nonparametrics” by Bower et al.","authors":"K. Rice, T. Lumley","doi":"10.1080/00031305.2023.2172078","DOIUrl":"https://doi.org/10.1080/00031305.2023.2172078","url":null,"abstract":"While we welcome Bower et al.’s (2022) exploration of how teaching need not rely on parametric methods alone, we wish to raise some issues with their presentation. First, “nonparametric”—meaning methods that do not rely on an assumed form of frequency distribution—is not synonymous with “rank-based.” When, as in Bower et al.’s (2022) examples, interest lies in differences in mean or median between groups, we could nonparametrically use permutation tests with test statistics that—straightforwardly—describe differences in sample mean or median between groups. These exact approaches use no assumptions other than independence of the outcomes (Berry, Johnston, and Mielke 2019, sec. 3.3) and that the test statistic being used captures deviations from the null that are of some scientific interest. So there is no need to switch to less-relevant rank-based methods, much less present them as the natural alternative to being parametric. We do agree with Bower et al. (2022) that user-friendly implementations are important, but permutation tests are available via simple R commands (e.g., the coin package’s oneway_test() function (Hothorn et al. 2008)) and shiny applications that are built on them. Second, the Kruskal-Wallis and Wilcoxon tests are not tests for population mean rank in the same sense that ANOVA and the t-test are tests for the mean, or Mood’s test is a test for the median. The issue is that the population mean and median for a subgroup are defined by the distribution of the response in just that subgroup. The mean rank, in contrast, depends on the distribution of responses in all subgroups and their sample sizes, so whether group 1 has higher mean rank than group 2 can depend on which other groups are also in the dataset. When the groups are not stochastically ordered, this leads to surprisingly complicated behavior of the Kruskal-Wallis test (Brown and Hettmansperger 2002). Finally, with regard to pedagogy we recommend the Data Problem-Solving Cycle (Wild and Pfannkuch 1999) in which the first step, “Problem,” identifies the question to address. This","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131096062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Response to Rice and Lumley 对赖斯和拉姆利的回应

The American Statistician Pub Date : 2023-04-03 DOI: 10.1080/00031305.2023.2182362

Roy Bower, William Cipolli

引用次数: 0

Mapping life expectancy loss in Barcelona in 2020 绘制2020年巴塞罗那预期寿命损失图

The American Statistician Pub Date : 2023-04-03 DOI: 10.1080/00031305.2023.2197022

X. Puig, J. Ginebra

引用次数: 0

Handbook of Multiple Comparisons 多重比较手册

The American Statistician Pub Date : 2023-04-03 DOI: 10.1080/00031305.2023.2198355

Junyong Park

{"title":"Handbook of Multiple Comparisons","authors":"Junyong Park","doi":"10.1080/00031305.2023.2198355","DOIUrl":"https://doi.org/10.1080/00031305.2023.2198355","url":null,"abstract":"Finite population sampling has found numerous applications in the past century. Validity inference of real populations is possible based on known sampling probabilities, “irrespectively of the unknown properties of the target population studied” (Neyman, 1934). Graphs allow one to incorporate the connections among the population units in addition. Many socio-economic, biological, spatial, or technological phenomena exhibit an underlying graph structure that may be the central interest of study, or the edges may effectively provide access to those nodes that are the primary targets. Either way, graph sampling provides a universally valid approach to studying realvalued graphs. This book establishes a rigorous conceptual framework for graph sampling and gives a unified presentation of much of the existing theory and methods, including several of the most recent developments. The most central concepts are introduced in Chapter 1, such as graph totals and parameters as targets of estimation, observation procedures following an initial sample of nodes that drive graph sampling, sample graph in which different kinds of induced subgraphs (such as edge, triangle, 4circle, K-star) can be observed, and graph sampling strategy consisting of a sampling method and an associated estimator. Chapters 2–4 introduce strategies based on bipartite graph sampling and incidence weighting estimator, which encompass all the existing unconventional finite population sampling methods, including indirect, network, adaptive cluster, or line intercept sampling. This can help to raise awareness of these methods, allowing them to be more effectively studied and applied as cases of graph sampling. For instance, Chapter 4 considers how to apply adaptive network sampling in a situation like the covid outbreak, which allows one to combat the virus spread by testtrace and to estimate the prevalence at the same time, provided the necessary elements of probability design and observation procedure are implemented. Chapters 5 and 6 deal with snowball sampling and targeted random walk sampling, respectively, which can be regarded as probabilistic breath-first or depth-first non-exhaustive search methods in graphs. Novel approaches to sampling strategies are developed and illustrated, such as how to account for the fact that an observed triangle could have been observed in many other ways that remain hidden from the realized sample graph, or how to estimate a parameter related to certain finiteorder subgraphs (such as a triangle) based on a random walk in the graph. The Bibliographic Notes at the end of each chapter contain some reflections on sources of inspiration, motivations for chosen approaches, and topics for future development. I found that the contents of the book are highly innovative and useful. The indirect sampling of Lavillee (2007) can be viewed as a special case of graph sampling. The materials in adaptive cluster sampling should be very useful in many real-world sampling","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127908484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Graph Sampling 图抽样

The American Statistician Pub Date : 2023-04-03 DOI: 10.1080/00031305.2023.2198354

Jae-Kwang Kim

引用次数: 0

Bartroff, J., Lorden, G. and Wang, L. (2022), “Optimal and Fast Confidence Intervals for Hypergeometric Successes,” The American Statistician: Comment by Schilling Bartroff, J, Lorden, G.和Wang, L.(2022)，“超几何成功的最佳和快速置信区间”，美国统计学家:Schilling评论

The American Statistician Pub Date : 2023-03-30 DOI: 10.1080/00031305.2023.2197021

M. Schilling

{"title":"Bartroff, J., Lorden, G. and Wang, L. (2022), “Optimal and Fast Confidence Intervals for Hypergeometric Successes,” The American Statistician: Comment by Schilling","authors":"M. Schilling","doi":"10.1080/00031305.2023.2197021","DOIUrl":"https://doi.org/10.1080/00031305.2023.2197021","url":null,"abstract":"The article “Optimal and Fast Confidence Intervals for Hypergeometric Successes” by Bartroff, J., Lorden, G. and Wang, L. (BLW) develops a procedure for interval estimation of the number of successes M in a finite population based on constructing minimal length symmetrical acceptance intervals, which are inverted to determine confidence intervals based on the number of successes x obtained from a sample of size n. The authors compare their procedure to previously developed methods derived from the method of pivoting (Buonaccorsi 1987; Konijn 1973; Casella and Berger 2002, chap. 9) as well as to the more recent work of Wang (2015), and show that their approach generally leads to substantially shorter confidence intervals than those of these competitors, while frequently achieving higher coverage. However, the present authors BLW were evidently unaware of my recent paper with A. Stanley, “A New Approach to Precise Interval Estimation for the Parameters of the Hypergeometric Distribution” (Schilling and Stanley 2020), which solved the problem of constructing a hypergeometric confidence procedure that has minimal length (that is, minimal total cardinality of the confidence intervals for x = 0 to n), while maximizing coverage among all length minimizing procedures. We also compared our method to the same competitors as those listed above, as well as to one that can be obtained from Blaker’s (2000) method, and we showed the superiority in performance of our procedure. The two goals of our paper—length minimization and maximal coverage—are the same as those in BLW’s paper, and BLW’s approach matches rather closely with ours. The authors’ “α optimal” is our “minimal cardinality,” while our “maximal coverage” is BLW’s “PM-maximizing.” The only substantive difference between the two confidence procedures is that BLW’s specifies symmetrical acceptance sets, while ours does not. This affects only a small number of confidence intervals. An investigation of all 95% confidence intervals for each population size N between 5 and 100 and sample sizes n = 5, 10, . . . with n ≤ N finds that BLW’s confidence intervals are identical to ours in 99.43% of the 34,200 intervals checked. When they are different, the BLW","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132865500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Correction: Linearity of Unbiased Linear Model Estimators 修正:无偏线性模型估计器的线性

The American Statistician Pub Date : 2023-03-27 DOI: 10.1080/00031305.2023.2184423

{"title":"Correction: Linearity of Unbiased Linear Model Estimators","authors":"","doi":"10.1080/00031305.2023.2184423","DOIUrl":"https://doi.org/10.1080/00031305.2023.2184423","url":null,"abstract":"The author presented a proof that a regression estimator unbiased for all distributions in a sufficiently broad family F0 must be linear. The family was taken to consist of the convolutions of all two-point distributions with a scale-family of smooth densities tending to a point mass at zero. The basic calculations were based solely on the discrete distributions, but the convolutions were introduced so that the family would be a subset of some standard, smooth nonparametric families. For example, adaptive estimation requires enough smoothness so that the Cramér-Rao bound provides optimal asymptotics. Some further comments appear in the supplemental material. The proof required that convergence of the smooth densities to zero implied that the expectations under the smooth convolutions converged to the expectation under the two-point distribution. This requires that the estimate be continuous, and there was a major error in the proof that unbiasedness implies continuity. It appears that continuity cannot be proved using unbiasedness over F0 , but it can be proved using unbiasedness over families of discrete distributions (see supplemental material). Thus, either the estimator must be assumed to be continuous, or a result using only discrete distributions is required. In trying to correct the error, a much simpler proof of the linearity result was found. This proof takes F0 to consist only of discrete distributions. The details are also presented in the supplemental material, but the basic idea is relatively simple: Consider a simplex with center at zero. Each point in the simplex (say −y ) is a convex combination of the vertices of the simplex; that is, −y is the expectation for a (discrete) distribution putting probability pi on vertex zi . Thus, the distribution putting probability 2 on y and 1 2 pi on zi has mean zero. Therefore, by unbiasedness, T(y) is a convex combination of the {T(zi)} ; that is, T(y) is the matrix whose columns are T(zi) times a vector, p , of probabilities. By basic properties of a simplex, p is an affine function of −y ; and so T(y) is an affine function of y . By unbiasedness under a point mass at zero, T(0) = 0 ; and so the affine constant is zero and T must be linear.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123041885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0