Showing papers on "Equivalence (measure theory) published in 2021"
TL;DR: It is proved that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights, implying that in contrast to the popular belief, the 2FE estimation does not represent a design-based, nonparametric estimation strategy for causal inference.
Abstract: The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ability of the 2FE model to simultaneously adjust for these two types of unobserved confounders critically relies upon the assumption of linear additive effects. Another common justification for the use of the 2FE estimator is based on its equivalence to the difference-in-differences estimator under the simplest setting with two groups and two time periods. We show that this equivalence does not hold under more general settings commonly encountered in applied research. Instead, we prove that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights. These analytical results imply that in contrast to the popular belief, the 2FE estimator does not represent a design-based, nonparametric estimation strategy for causal inference. Instead, its validity fundamentally rests on the modeling assumptions.
192 citations
TL;DR: It is argued that the fact that for any model from one class there is an equivalent model from the other class does not mean that both models are equally plausible accounts of the data-generating mechanism.
Abstract: Networks are gaining popularity as an alternative to latent variable models for representing psychological constructs. Whereas latent variable approaches introduce unobserved common causes ...
86 citations
28 Jan 2021
TL;DR: In this article, the authors argue that decisions made by researchers while analyzing data (e.g., how to measure variables, how to handle outliers) are sometimes arbitrary, without an objective justification for choosing one alternative.
Abstract: Decisions made by researchers while analyzing data (e.g., how to measure variables, how to handle outliers) are sometimes arbitrary, without an objective justification for choosing one alternative ...
48 citations
TL;DR: The equivalence between the two-way fixed effects estimator and an estimator obtained from a pooled ordinary least squares regression that includes unit-specific time averages and time-period specific cross-sectional averages was established in this article.
Abstract: I establish the equivalence between the two-way fixed effects (TWFE) estimator and an estimator obtained from a pooled ordinary least squares regression that includes unit-specific time averages and time-period specific cross-sectional averages, which I call the two-way Mundlak (TWM) regression. This equivalence furthers our understanding of the anatomy of TWFE, and has several applications. The equivalence between TWFE and TWM implies that various estimators used for intervention analysis – with a common entry time into treatment or staggered entry, with or without covariates – can be computed using TWFE or pooled OLS regressions that control for time-constant treatment intensities, covariates, and interactions between them. The approach allows considerable heterogeneity in treatment effects across treatment intensity, calendar time, and covariates. The equivalence implies that standard strategies for heterogeneous trends are available to relax the common trends assumption. Further, the two-way Mundlak regression is easily adapted to nonlinear models such as exponential models and logit and probit models.
42 citations
TL;DR: In this paper, the equivalence of equivariant K-polystability with geometric K-semistability was proved. And the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs were proved.
Abstract: We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs.
35 citations
TL;DR: In this article, a simple and elegant bijection between metric and kernel is proposed to better preserve the similarity structure, allow distance correlation and Hilbert-Schmidt independence criterion to be always the same for hypothesis testing, streamlines the code base for implementation, and enables a rich literature of distance-based and kernel-based methodologies to directly communicate with each other.
Abstract: Distance correlation and Hilbert-Schmidt independence criterion are widely used for independence testing, two-sample testing, and many inference tasks in statistics and machine learning. These two methods are tightly related, yet are treated as two different entities in the majority of existing literature. In this paper, we propose a simple and elegant bijection between metric and kernel. The bijective transformation better preserves the similarity structure, allows distance correlation and Hilbert-Schmidt independence criterion to be always the same for hypothesis testing, streamlines the code base for implementation, and enables a rich literature of distance-based and kernel-based methodologies to directly communicate with each other.
35 citations
TL;DR: A stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC) is developed and the equivalence among asymptotical stability in mean square, stochastic stability (SS), exponential stability inmean square (ESMS), and ESMS-C has been established.
Abstract: In this paper, we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC). Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning (ESMS-C) are derived via linear matrix inequalities (LMIs), which can be examined conveniently. Under novel sufficient conditions, the equivalence among asymptotical stability in mean square (ASMS), stochastic stability (SS), exponential stability in mean square (ESMS), and ESMS-C has been established. Besides, numerical simulations are employed in result validation.
30 citations
TL;DR: In this article, the authors revisited a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem, and introduced some optimizations and provided a security analysis for all variants considered.
Abstract: Code-based cryptographic schemes are highly regarded among the quantum-safe alternatives to current standards. Yet, designing code-based signatures using traditional methods has always been a challenging task, and current proposals are still far from the target set by other post-quantum primitives (e.g. lattice-based). In this paper, we revisit a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem. We introduce some optimizations and provide a security analysis for all variants considered. We then show that the new parameters produce instances of practical interest.
28 citations
15 Jun 2021
TL;DR: In this article, the authors consider the sequential sampling model and characterize the classes which admit a uniform law of large numbers in this model, and show that these classes are exactly the classes that are online learnable.
Abstract: Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can affect the environment they are acting upon and interact with it. Specifically, we consider the sequential sampling model proposed by Ben-Eliezer and Yogev (2020), and characterize the classes which admit a uniform law of large numbers in this model: these are exactly the classes that are online learnable. Our characterization may be interpreted as an online analogue to the equivalence between learnability and uniform convergence in statistical (PAC) learning. The sample-complexity bounds we obtain are tight for many parameter regimes, and as an application, we determine the optimal regret bounds in online learning, stated in terms of Littlestone’s dimension, thus resolving the main open question from Ben-David, Pal, and Shalev-Shwartz (2009), which was also posed by Rakhlin, Sridharan, and Tewari (2015).
28 citations
TL;DR: In this paper, the strong equivalence between projected Wasserstein metrics and the classical one was shown for p = 1, where p is the number of vertices in the projected metric.
Abstract: The sliced Wasserstein metric Wp and more recently max-sliced Wasserstein metric W‾p have attracted abundant attention in data sciences and machine learning due to their advantages to tackle the curse of dimensionality, see e.g. [15], [6]. A question of particular importance is the strong equivalence between these projected Wasserstein metrics and the (classical) Wasserstein metric Wp. Recently, Paty and Cuturi have proved in [14] the strong equivalence of W‾2 and W2. We show that the strong equivalence also holds for p=1, while the sliced Wasserstein metric does not share this nice property.
26 citations
TL;DR: In this paper, a parallel domain decomposition method is proposed for solving the Stokes-Darcy coupled problem with the Beavers-Joseph-Saffman (BJS) interface conditions.
TL;DR: In this article, the authors compare three approaches for finding evidence for equivalence: the frequentist two one-sided tests procedure, the Bayesian highest density interval region of practical equivalence procedure, and the Bayes factor interval null procedure.
Abstract: Some important research questions require the ability to find evidence for two conditions being practically equivalent. This is impossible to accomplish within the traditional frequentist null hypothesis significance testing framework; hence, other methodologies must be utilized. We explain and illustrate three approaches for finding evidence for equivalence: The frequentist two one-sided tests procedure, the Bayesian highest density interval region of practical equivalence procedure, and the Bayes factor interval null procedure. We compare the classification performances of these three approaches for various plausible scenarios. The results indicate that the Bayes factor interval null approach compares favorably to the other two approaches in terms of statistical power. Critically, compared with the Bayes factor interval null procedure, the two one-sided tests and the highest density interval region of practical equivalence procedures have limited discrimination capabilities when the sample size is relatively small: Specifically, in order to be practically useful, these two methods generally require over 250 cases within each condition when rather large equivalence margins of approximately .2 or .3 are used; for smaller equivalence margins even more cases are required. Because of these results, we recommend that researchers rely more on the Bayes factor interval null approach for quantifying evidence for equivalence, especially for studies that are constrained on sample size. (PsycInfo Database Record (c) 2021 APA, all rights reserved).
07 Jan 2021
Abstract: The .interplay of �etaphor and re?l:i.ty contributes notably to · La Celestina' s iniaginative power.l: Two justly fmnous cases are those of real and metaphorical fall!¡l, ancl. of locus amoenus im�gery as an alternately iyri.cal and. sínister. coun terpar.t to M. elibea' s · . g·ai·den (which is · at once _a real place and an image for Melibea' s b�dy :·· Act· XX, P.�. ·230). 2 -Of equal importance, though. less ofte� no tice9; is· the _connec.tion of. thre!:!_real (and, as I hope to show, e.quivalent) ob jects with a cluster·qf image�. The �bjeits are Celestina's .skein of thread (Acts· III:..IV), Me libea' ·s girdle. (IV-VI), an.d Calisto' s gold chain (XI-XII), and the images are those of hunting¡ �rapping, and captivity. For example:
29 Jun 2021
TL;DR: In this article, a categorical formulation of Lovasz' theorem was proposed, which applies to any locally finite category with pushouts and a proper factorization system, and it is shown that it can be generalized to modal logic.
Abstract: Lovasz (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B for any finite structure C. Soon after, Pultr (1973) proved a categorical generalisation of this fact. We propose a new categorical formulation, which applies to any locally finite category with pushouts and a proper factorisation system. As special cases of this general theorem, we obtain two variants of Lovasz' theorem: the result by Dvorak (2010) that characterises equivalence of graphs in the k-dimensional Weisfeiler-Leman equivalence by homomorphism counts from graphs of tree-width at most k, and the result of Grohe (2020) characterising equivalence with respect to first-order logic with counting and quantifier depth k in terms of homomorphism counts from graphs of tree-depth at most k. The connection of our categorical formulation with these results is obtained by means of the game comonads of Abramsky et al. We also present a novel application to homomorphism counts in modal logic.
TL;DR: Eggers et al. as discussed by the authors developed two equivalence tests tailored for regression discontinuity (RD) designs that allow researchers to provide statistical evidence that the design is credible, using a null of no difference in the parameter of interest at the discontinuity.
Abstract: Regression discontinuity (RD) designs are increasingly common in political science. They have many advantages, including a known and observable treatment assignment mechanism. The literature has emphasized the need for “falsification tests” and ways to assess the validity of the design. When implementing RD designs, researchers typically rely on two falsification tests, based on empirically testable implications of the identifying assumptions, to argue the design is credible. These tests, one for continuity in the regression function for a pretreatment covariate, and one for continuity in the density of the forcing variable, use a null of no difference in the parameter of interest at the discontinuity. Common practice can, incorrectly, conflate a failure to reject evidence of a flawed design with evidence that the design is credible. The well-known equivalence testing approach addresses these problems, but how to implement equivalence tests in the RD framework is not straightforward. This paper develops two equivalence tests tailored for RD designs that allow researchers to provide statistical evidence that the design is credible. Simulation studies show the superior performance of equivalence-based tests over tests-of-difference, as used in current practice. The tests are applied to the close elections RD data presented in Eggers et al. (2015b).
TL;DR: In this paper, the authors employ German household expenditure data to estimate equivalence scales using several parametric, semiparametric, and nonparametric approaches, and find that some approaches yield more plausible results than others while implausible scales are mostly based on linear Engel curves.
Abstract: Equivalence scales are routinely applied to adjust the income of households of different sizes and compositions. Because of their practical importance for the measurement of inequality and poverty, a large number of methods for the estimation of equivalence scales have been proposed. Until now, however, no comprehensive comparison of current methods has been conducted. In this paper, we employ German household expenditure data to estimate equivalence scales using several parametric, semiparametric, and nonparametric approaches. Using a single dataset, we find that some approaches yield more plausible results than others while implausible scales are mostly based on linear Engel curves. The results we consider plausible are close to the modified OECD scale, and to the square root scale for larger households.
TL;DR: In this article, distributionally robust optimization involves various probability measures in its problem formulation, which can be bundled to constitute a risk functional, and for this equivalence, risk functionals co...
Abstract: Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals co...
TL;DR: Mean value formulas are of great importance in the theory of partial differential equations: many very useful results are drawn, for instance, from the well-known equivalence between harmonic functs.
Abstract: Mean value formulas are of great importance in the theory of partial differential equations: many very useful results are drawn, for instance, from the well-known equivalence between harmonic funct
TL;DR: This paper argued that the self-love that motivates exchange in The Wealth of Nations can be seen as the desire for deserved approval discussed by Adam Smith in The Theory of Moral Sentiments (TMS).
Abstract: This article argues that the self-love that motivates exchange in The Wealth of Nations (WN) can be seen as the desire for deserved approval discussed by Adam Smith in The Theory of Moral Sentiments (TMS). This often overlooked desire appears in TMS as the most representative kind of self-love. Exchange motivated by this desire emerges as the way to find confirmation through others’ appraisal of one’s own self-assessment, and thus to find an agreed-upon measure for respective deserved praise. The target in this economic relationship is that equivalence that signals mutual recognition of deserved esteem. Equivalence here is the aim and not the result of exchange, unlike a tug-of-war, where both parties try to give as little and gain as much as possible regardless of the recognition each deserves.
TL;DR: The Poisson stick process-based vehicular network is equivalent to the Poisson line process- based and Poisson lilypond model- based vehicular networks, and their rotational variants, as well as other models in terms of reliability.
Abstract: We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of $\mathbb {R}^{2}$ . The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street. Models in this Coxian framework can characterize streets of different lengths and orientations forming intersections or T-junctions. The lengths of the streets can be infinite or finite and mutually independent or dependent. We analyze the reliability of communication for different models, where reliability is the probability that a vehicle at an intersection, a T-junction, or a general location can receive a message successfully from a transmitter at a certain distance. Further, we introduce a notion of equivalence between vehicular models, which means that a representative model can be used as a proxy for other models in terms of reliability. Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants.
TL;DR: The equivalence canonical form of five quaternion matrices is investigated and five color images can be encrypted simultaneously by using this equivalences canonical form.
TL;DR: In this article, the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach was demonstrated.
Abstract: This paper shows the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach. Both formulations allow solving the load flow problem in meshed and radial distribution grids even if these are operated with alternating current (AC) or direct current (DC) technologies. Both load flow methods are completely described in this research to make a fair comparison between them and demonstrate their equivalence. Numerical comparisons in the 33- and 69-bus test feeder with radial topology show that both methods have the same number of iterations to find the solution with a convergence error defined as 1×10−10.
TL;DR: In this article, the authors used results from a name perception study paired with an original correspondence audit experiment of U.S. state legislators to show that names manipulate perceptions of minority status, socioeconomic status (SES), and migrant status.
Abstract: Abstract Name-based treatments have been used in observational studies and experiments to study the differential effect of identity—commonly race or ethnic minority status. These treatments are typically assumed to signal only a single characteristic. If names unintentionally signal other characteristics, then the treatment can violate information equivalence, and estimated treatment effects cannot be attributed to the desired characteristic alone. Using results from a name perception study paired with an original correspondence audit experiment of U.S. state legislators, we show that names manipulate perceptions of minority status, socioeconomic status (SES), and migrant status. Our audit study shows that low SES status is related to reply rates both across and within each racial category. These results provide evidence that discrimination cannot be easily attributed singularly to the intended treatment of minority status but rather reflect a more multifaceted form of discrimination. More generally, our results provide an example of how name-based treatments manipulate more than the intended characteristic, which means that estimated treatment effects cannot be interpreted as being manipulated solely by the desired characteristic. Future studies with name-based or other informational treatments should account for the potential violation of information equivalence in their research design and interpretation of results.
TL;DR: In this article, the equivalence of the coefficients from the full and partial regressions of the Frisch-Waugh-Lovell Theorem was shown for model-based and design-based standard errors.
29 Apr 2021
TL;DR: Gideon Toury as mentioned in this paper distinguishes among various socio-cultural norms in the receiving situation which "constrain" the translator's choices and strategies and delimit concepts of equivalence.
Abstract: Gideon Toury’s chapter, first published in 1978, distinguishes among various socio-cultural “norms” in the receiving situation which “constrain” the translator’s choices and strategies and delimit concepts of equivalence. Norms can be inferred through “shifts” that occur between the translation and the source text. Toury seeks to describe and explain the “acceptability” of the translated text, the ways in which various shifts constitute a type of equivalence that reflects receptor norms held by specific cultural constituencies at a certain historical moment.
TL;DR: This research sought to assess the psychometric properties of the French versions of the Body checking Questionnaire and the Body Checking Cognitions Scale among community samples and supported the criterion-related validity of ratings on both measures with measures of global self-esteem, physical appearance, social physique anxiety, fear of negative appearance evaluation, and disturbed eating attitudes and behaviors.
Abstract: This research sought to assess the psychometric properties of the French versions of the Body Checking Questionnaire and the Body Checking Cognitions Scale among community samples. A total sample of 922 adolescents and adults was involved in a series of two studies. The results from the first study supported factor validity and reliability of responses obtained on these two measures, and showed that both measures were best represented by a bifactor-exploratory structural equation modeling representation of the data. The results from the second study replicated these conclusions, while also supporting the measurement invariance of the bifactor-exploratory structural equation modeling solution and the equivalence of the correlations among the two measures (i.e., convergent validity) across samples. This second study also supported the criterion-related validity of ratings on both measures with measures of global self-esteem, physical appearance, social physique anxiety, fear of negative appearance evaluation, and disturbed eating attitudes and behaviors. Finally, the results of this last study also supported the measurement invariance and lack of differential item functioning of both measures in relation to sex, age, diagnosis of eating disorders, and body mass index.
02 May 2021
TL;DR: In this article, the notion of AMENITY for partial actions and Fell bundles over discrete groups was introduced and studied, and it was shown that the cross-sectional $$C^*$$ -algebra of a Fell bundle is nuclear if and only if the underlying unit fibre was nuclear and the Fell bundle was AD-amenable.
Abstract: Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. We prove that the cross-sectional $$C^*$$
-algebra of a Fell bundle is nuclear if and only if the underlying unit fibre is nuclear and the Fell bundle is AD-amenable. If a partial action is globalisable, then it is AD-amenable if and only if its globalisation is AD-amenable. Moreover, we prove that AD-amenability is preserved by (weak) equivalence of Fell bundles and, using a very recent idea of Ozawa and Suzuki, we show that AD-amenability is equivalent to an approximation property introduced by Exel.
TL;DR: In this paper, a measurement technique for determination of equivalence ratio fluctuations from flame chemiluminescence in a kerosene-fuelled lean premixed combustor under atmospheric conditions is presented.
Abstract: In this study a measurement technique for determination of equivalence ratio fluctuations from flame chemiluminescence in a kerosene-fuelled lean premixed combustor under atmospheric conditions is presented. Firstly, fundamental investigations into the relationship between the ratio of different chemiluminescence signals and the equivalence ratio are carried out using an imaging spectrometer. The chemiluminescence intensity is recorded for a wide range of equivalence ratios and fuel mass flows during steady state operation. The spectra show that the CH*/OH* ratio depends linearly on the equivalence ratio and is independent of the mass flow in the investigated range. Moreover, the background radiation has no influence on the monotonous trend of the CH*/OH* ratio for kerosene combustion. This interesting finding opens up new possibilities for passive optical measurement of the equivalence ratio in kerosene flames. Bandpass-filtered phase-correlated images of OH* and CH* chemiluminescence of an acoustically excited flame are taken simultaneously on one camera chip using an image doubler. After distortion correction, the image pair is used to calculate the global equivalence ratio from the CH*/OH* ratio. Based on the calibration chart derived in stationary operation, phase-resolved equivalence ratio perturbations are determined during acoustic excitation. The presented technique allows a quantitative measurement of equivalence ratio fluctuations in spray combustion and can therefore provide a better understanding of the fundamental mechanisms of thermoacoustic instabilities triggered by equivalence ratio fluctuations.
TL;DR: These theoretical results provide error-bound guarantees for TWD, together with a formal construction to define cost-sensitive cautious classifiers based on CP, and show that the proposed techniques can be used to obtain cautious learning classifiers that are competitive with, and often out-perform, state-of-the-art approaches.