A Joint Confidence Region for an Overall Ranking of Populations

Kampel, Martin; Wright, Thomas; Wieczorek, Jerzy

doi:10.1111/rssc.12402

Cited by 20 publications

(65 citation statements)

References 13 publications

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“…Our paper aligns with the frequentist literature on incorporating uncertainty into rankings (Andrews et al, 2019;Klein et al, 2020;Xie et al, 2009). One recent paper that is highly related to our own is Mogstad et al (2021) which proposes frequentist methods for constructing marginal confidence sets for both the rank of a single subject and the joint rankings of all subjects.…”

Section: Discussionsupporting

confidence: 65%

Measuring the spatial distribution of health rankings in the United States

Davis

Gordan²,

Tchernis

2021

Health Economics

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Both the prevalence and importance of rankings have grown considerably in cases where a characteristic cannot be captured using a single variable. A prime candidate for the use of rankings is county-level health in the United States. Given county health's multidimensional nature, researchers, policymakers, and other stakeholders regularly use rankings to combine information from multiple sources into a single outcome. The most commonly used county health rankings (CHRs) are the University of Wisconsin Population Health Institute's (UWPHI's) CHRs.Since 2010, the CHRs have been used to allocate scarce resources, design health policy, and demonstrate need for health improving interventions. In 2012, the San Bernardino County Health department used the CHRs to support their Healthy Communities initiatives program, offering $100,000 dollar seed grants to participating counties (County Health Rankings and Roadmaps, 2012a). In Lima Ohio, Active Allen County relied on the CHRs to engage with the Ohio Department of Public Health and local stakeholders to improve health in their county, receiving a $1.2 million Community Transformation grant from the Centers for Disease Control and Prevention (County Health Rankings and Roadmaps, 2013). The Greater Flint Health Coalition implemented a 10-year County Health Rankings Action Plan to

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Section: Discussionsupporting

confidence: 65%

Measuring the spatial distribution of health rankings in the United States

Davis

Gordan²,

Tchernis

2021

Health Economics

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“…Consider the case in which θ(P ) is a vector of expectations andθ the corresponding vector of sample means. Then, the two confidence sets R joint n in Lemma B.1, one using the critical value in (40) and the other the Bonferroni critical value in (41), coincide with the two proposals in Klein et al (2020). The simulations in Section 4 confirm the results in Lemma B.1 by showing that our confidence sets for ranks are either of similar or strictly smaller size than those by Klein et al (2020).…”

Section: Appendix B An Alternative Construction Of Confidence Sets Fosupporting

confidence: 61%

“…As mentioned previously, in each case, we begin by describing a simple construction that relies on simultaneous confidence sets for certain pairs of populations before showing how to improve upon this construction using an appropriately chosen multiple hypothesis testing problem. In Section 4, we examine the finite-sample behavior of our inference procedure via a simulation study, including a comparison with the method proposed by Klein et al (2020). Finally, in Section 5, we apply our inference procedures to re-examine the rankings of both developed countries in terms of academic achievement and neighborhoods in the United States in terms of intergenerational mobility.…”

Section: Introductionmentioning

confidence: 99%

Inference for ranks with applications to mobility across neighborhoods and academic achievement across countries

Mogstad¹,

Romano²,

Shaikh³

et al. 2021

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It is often desired to rank different populations according to the value of some feature of each population. For example, it may be desired to rank neighborhoods according to some measure of intergenerational mobility or countries according to some measure of academic achievement. These rankings are invariably computed using estimates rather than the true values of these features. As a result, there may be considerable uncertainty concerning the rank of each population. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each population. We consider both the problem of constructing marginal confidence sets for the rank of a particular population as well as simultaneous confidence sets for the ranks of all populations. We show how to construct such confidence sets under weak assumptions. An important feature of all of our constructions is that they remain computationally feasible even when the number of populations is very large. We apply our theoretical results to re-examine the rankings of both neighborhoods in the United States in terms of intergenerational mobility and developed countries in terms of academic achievement. The conclusions about which countries do best and worst at reading, math, and science are fairly robust to accounting for uncertainty. The confidence sets for the ranking of the 50 most populous commuting zones by mobility are also found to be small. However, the mobility rankings become much less informative if one includes all commuting zones, if one considers neighborhoods at a more granular level (counties, Census tracts), or if one uses movers across areas to address concerns about selection.

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“…Second, we propose a bootstrap method that accounts for the dependence in the estimators of the multinomial success probabilities. Our paper is also related to a recent paper by Klein et al (2020), who consider the problem of constructing confidence sets analogous to those in Mogstad et al (2020). We show how a modification of their procedure can also be used to construct confidence sets that are valid in finite samples in the presence of multinomial data.…”

Section: Introductionmentioning

confidence: 76%

Finite- and Large-Sample Inference for Ranks Using Multinomial Data with an Application to Ranking Political Parties

et al. 2021

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It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.

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A Joint Confidence Region for an Overall Ranking of Populations

Cited by 20 publications

References 13 publications

Measuring the spatial distribution of health rankings in the United States

Measuring the spatial distribution of health rankings in the United States

Inference for ranks with applications to mobility across neighborhoods and academic achievement across countries

Finite- and Large-Sample Inference for Ranks Using Multinomial Data with an Application to Ranking Political Parties

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