Mathematics eJournal最新文献

{"title":"Hot or Not? A Nonparametric Formulation of the Hot Hand in Baseball","authors":"Amanda K. Glazer, L. Goldberg","doi":"10.2139/ssrn.3562754","DOIUrl":"https://doi.org/10.2139/ssrn.3562754","url":null,"abstract":"A nonparametric analysis of player plate appearances (PA) in the 2018 Major League Baseball (MLB) season provides no evidence of a batter hot hand. Players with more than 100 PAs in the 2018 season are analyzed using one-sided permutation tests stratified by player. Based on recent literature, we use the correlation between lagged on-base percentage (OBP)and a binary indicator of on-base performance. We discuss the strengths and weaknesses of this test statistic as well as others in the literature. A common criticism of no-hot-hand findings for individual players is low power, and a frequently proposed remedy is pooling data across players. Through simulation, we show that pooling data conflates long-term ability and recent performance. Another common criticism of no-hot-hand findings is emphasis on recent performance. We show that long lags, which de-emphasize recent performance, can lead to counter intuitive results. In contrast to much of the recent literature, which uses parametric methods, we argue that our nonparametric method is the most appropriate way to analyze the existence of the hot hand in baseball as well as numerous other inference questions.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129126943","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}

{"title":"The Lognormal Characteristic Function","authors":"Andrew P. Leung","doi":"10.2139/ssrn.3550403","DOIUrl":"https://doi.org/10.2139/ssrn.3550403","url":null,"abstract":"A simple expression for the characteristic function of the lognormal distribution has eluded researchers. This is useful for computing the sum of lognormal variables, either with each other or with other statistical variables. In this paper, we provide a simple formula for the characteristic function.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121494942","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}

{"title":"Financial Risk Taking in the Presence of Correlated Non-Financial Background Risk","authors":"W. Chiu","doi":"10.2139/ssrn.3175824","DOIUrl":"https://doi.org/10.2139/ssrn.3175824","url":null,"abstract":"This paper characterizes the stochastic deterioration resulting from taking a zero-mean financial risk in the presence of correlated non-financial background risk. We show in particular that it has an equivalent stochastic order as well as a necessary and sufficient \"integral condition'' that implies and is implied by a particular sense in which the stochastic deterioration can be decomposed into a \"correlation increase'' and a \"marginal risk increase''. We further characterize a measure of aversion to the stochastic deterioration. These characterizations provide for a more general framework for formulating concepts of increases in risk and correlation and for better understanding risk management decisions governed by individuals' attitudes to them.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132395439","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}

{"title":"Riemann Hypothesis - A Simple Proof with a Deeper Meaning","authors":"Joaquin Agatiello","doi":"10.2139/ssrn.3550793","DOIUrl":"https://doi.org/10.2139/ssrn.3550793","url":null,"abstract":"A long sought-after result is achieved after following an original idea of mine which turned out to unveil what was apparently hidden in Riemann’s invariant functional equation and more.<br><br>In this process, certain aspects of Riemann zeta function’s equations and their calculations are discussed as well as the meaning and significance of the results obtained herein.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116554232","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}

{"title":"On Stable and Efficient Mechanisms for Priority-Based Allocation Problems","authors":"Kang Rong, Qianfeng Tang, Yongchao Zhang","doi":"10.2139/ssrn.3077761","DOIUrl":"https://doi.org/10.2139/ssrn.3077761","url":null,"abstract":"Abstract For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof ( Ergin, 2002 ). We reveal a hidden iterative removal structure behind such deferred acceptance algorithms. A nonempty set of students is called a top fair set (TFS) if when all students apply to their most preferred schools and all schools accept the best applicants up to their quotas, students in the set are always accepted, regardless of other students' preferences. We provide an elimination process to find the maximal TFS, if any TFS exists. We show that for any priority structure, iterative removal of TFS is equivalent to the associated deferred acceptance algorithm if and only if the latter is a Pareto efficient mechanism.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130696969","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}

{"title":"Subjective Probability Does Not Exist","authors":"A. Zaman","doi":"10.2139/ssrn.3496823","DOIUrl":"https://doi.org/10.2139/ssrn.3496823","url":null,"abstract":"We show that the rationality arguments used to establish the existence of subjective probabilities depend essentially on the identification of acting-as-ifyou-believe and actually believing. We show that these two ideas, the pretense of knowledge about probabilities, and actual knowledge about probabilities, can easily be distinguished outside the restricted context of choice over special types of lotteries. When making choices over Savage-type lotteries, rational agents will act as if they know their subjective probabilities for uncertain events, but they will reveal their ignorance in other decision making contexts. This means that subjective probabilities cannot be assumed to exist, except when there is objective warrant for them.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122747967","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}

{"title":"Instrument Residual Estimator for Any Response with Endogenous Binary Treatment","authors":"Myoung‐jae Lee","doi":"10.2139/ssrn.3495756","DOIUrl":"https://doi.org/10.2139/ssrn.3495756","url":null,"abstract":"Given a binary treatment D, a response Y with its potential versions (Y⁰,Y¹) and covariates X, often D is endogenous. Unless Y is continuous, dealing with a binary endogenous D has been difficult even when an instrument δ is available. This paper shows that, for any form of Y (binary, ordinal, censored, continuous, ...), we always have a linear representation Y=μ₀(X)+μ₁(X)D+error with E(error|δ,X)=0, where μ₀(X) is an unknown 'X-conditional intercept' and μ₁(X)≡E(Y¹-Y⁰|complier,X) is the unknown 'X-conditional slope/effect'. We propose 'instrumental residual estimator (IRE)' using δ-E(δ|X) as an instrument for D. IRE is consistent for the Cov(δ,D|X)-weighted average of E(Y¹-Y⁰|complier,X), which screens out individuals with weak instruments in the sense of small |Cov(δ,D|X)|. IRE is easy to implement, and has an asymptotic variance estimator that works well in small samples as a simulation study demonstrates. If desired, a 'weighted IRE' can be used as well to estimate E{E(Y¹-Y⁰|complier,X)}.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130141697","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}

{"title":"Conditional Value at Risk and Partial Moments for the Metalog Distributions","authors":"V. Khokhlov","doi":"10.2139/ssrn.3777921","DOIUrl":"https://doi.org/10.2139/ssrn.3777921","url":null,"abstract":"The metalog distributions represent a convenient way to approach many practical application. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to the tail conditional expectations. It also addressed the derivation of the first-order partial moments and shows that they are convex with respect to the vector of the metalog distribution parameters.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133855555","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}

{"title":"An Examination of P. Davidson’s Misunderstandings about the Limiting Frequency Theory of Probability, Ergodicity and Non Ergodicity: These Approaches Require that either the Number of Observations Approaches Infinity or Time Approaches Infinity in Order for the Limit to Exist","authors":"M. E. Brady","doi":"10.2139/ssrn.3471024","DOIUrl":"https://doi.org/10.2139/ssrn.3471024","url":null,"abstract":"Paul Davidson’s technical understanding of the mathematical details of the Limiting Frequency theory of probability and Kolmogorov’s measure theoretic extension from additivity to countable additivity, which allows for an extension of the concept of the Law of Large Numbers to the concept or ergodicity and non ergodicity, where time is substituted for observations, is extremely poor.<br><br>Davidson has repeatedly made errors in many journal articles published in the Journal of Post Keynesian Economics and books published by Edward Elgar about these concepts since 1979. For instance, one example of a fundamental error made by Davidson since 1982 is his assertion, contradicted by all mathematical statisticians, that “Non stationarity is a sufficient, but not a necessary, condition for nonergodicity”. Davidson has repeated this false claim many times in the literature since 1982 when it first appeared in an article published in the Journal of Post Keynesian Economics. It is very simple to grasp what Davidson’s fundamental error is from just the title of a 1973 paper published in The Annals of Probability by R W Madsen and D L Isaacson, titled “Strongly Ergodic Behavior for Non-Stationary Markov Processes”, to realize that the correct mathematical statement is that non-stationary processes can be ergodic. This means that the correct analysis, known for certain by all mathematical statisticians since 1973, is that “Non stationarity is a necessary, but not a sufficient, condition for nonergodicity”.<br><br>There is no existing evidence that Paul Davidson had any knowledge of Keynes’s approach to measurement, which rejected the exact and precise approach of Kolmogorov and Tinbergen except as a very special case, in favor of an inexact approach to measurement based on approximation and imprecise, interval valued probability and outcomes. Given that the concepts of ergodicity and non ergodicity require as a necessary condition the acceptance of the measure theoretic approach of Kolmogorov,it is straightforward to conclude that Keynes would reject the concepts of ergodicity and non ergodicity in macroeconomics or in regard to the concept of uncertainty because Part II of the TP establishes non additivity and non linearity as the general case and additivity and linearity as a special case, which is what the Kolmogorov axioms require.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"605 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122364100","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}

{"title":"On Quadratic Forms in Multivariate Generalized Hyperbolic Random Vectors","authors":"S. Broda, Juan Arismendi-Zambrano","doi":"10.2139/ssrn.3369208","DOIUrl":"https://doi.org/10.2139/ssrn.3369208","url":null,"abstract":"\u0000 This article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (Gil-Pelaez, 1951). Two numerical applications are considered: the distribution of the two-stage least squares estimator and the expected shortfall of a quadratic portfolio.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124364718","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}