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Comparative R Squared 比较R平方
Mathematics eJournal Pub Date : 2021-03-31 DOI: 10.2139/ssrn.3790200
Min S. Kim
{"title":"Comparative R Squared","authors":"Min S. Kim","doi":"10.2139/ssrn.3790200","DOIUrl":"https://doi.org/10.2139/ssrn.3790200","url":null,"abstract":"This paper proposes a simple statistic for testing statistical significance of R squared. This statistic, called \"comparative R squared,\" also tests statistical significance of the difference of R squared between null and alternative models with additional explanatory variables. The asymptotic distribution of the test statistic is a chi square distribution with the degree of freedom equal to the number of (additional) explanatory variables. Unlike the F test, this statistic is useful when dealing with non-normality. Simulations show that the test statistic behaves well and has no distortion of size, even in small samples.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121803966","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: 4
Relevance 相关性
Mathematics eJournal Pub Date : 2021-03-10 DOI: 10.2139/ssrn.3803440
M. Czasonis, M. Kritzman, D. Turkington
{"title":"Relevance","authors":"M. Czasonis, M. Kritzman, D. Turkington","doi":"10.2139/ssrn.3803440","DOIUrl":"https://doi.org/10.2139/ssrn.3803440","url":null,"abstract":"The authors describe a new statistical concept called relevance from a conceptual and mathematical perspective, and based on their mathematical framework, they present a unified theory of relevance, regressions, and event studies. They also include numerical examples of how relevance is used to forecast.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124435825","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: 1
Investigation of Parameter Behaviors in Stationarity of Autoregressive and Moving Average Models through Simulations 自回归和移动平均模型平稳性参数行为的仿真研究
Mathematics eJournal Pub Date : 2020-12-15 DOI: 10.22377/AJMS.V4I4.295
A. Imam
{"title":"Investigation of Parameter Behaviors in Stationarity of Autoregressive and Moving Average Models through Simulations","authors":"A. Imam","doi":"10.22377/AJMS.V4I4.295","DOIUrl":"https://doi.org/10.22377/AJMS.V4I4.295","url":null,"abstract":"The most important assumption about time series and econometrics data is stationarity. Therefore, this study focuses on behaviors of some parameters in stationarity of autoregressive (AR) and moving average (MA) models. Simulation studies were conducted using R statistical software to investigate the parameter values at different orders (p) of AR and (q) of MA models, and different sample sizes. The stationary status of the p and q are, respectively, determined, parameters such as mean, variance, autocorrelation function (ACF), and partial autocorrelation function (PACF) were determined. The study concluded that the absolute values of ACF and PACF of AR and MA models increase as the parameter values increase but decrease with increase of their orders which as a result, tends to zero at higher lag orders. This is clearly observed in large sample size (n = 300). However, their values decline as sample size increases when compared by orders across the sample sizes. Furthermore, it was observed that the means values of the AR and MA models of first order increased with increased in parameter but decreased when sample sizes were decreased, which tend to zero at large sample sizes, so also the variances.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122252659","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: 1
Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions 给定风险因子边际分布的最大风险谱测度
Mathematics eJournal Pub Date : 2020-10-23 DOI: 10.2139/ssrn.3720332
Mario Ghossoub, Jesse Hall, D. Saunders
{"title":"Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions","authors":"Mario Ghossoub, Jesse Hall, D. Saunders","doi":"10.2139/ssrn.3720332","DOIUrl":"https://doi.org/10.2139/ssrn.3720332","url":null,"abstract":"We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSM), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSM admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115056888","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: 6
Notes on Ridge Functions and Neural Networks 脊函数和神经网络注释
Mathematics eJournal Pub Date : 2020-05-28 DOI: 10.2139/ssrn.3618165
V. Ismailov
{"title":"Notes on Ridge Functions and Neural Networks","authors":"V. Ismailov","doi":"10.2139/ssrn.3618165","DOIUrl":"https://doi.org/10.2139/ssrn.3618165","url":null,"abstract":"These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential equations (where they are called plane waves), computerized tomography and statistics. These functions are also the underpinnings of many central models in neural networks. \u0000We are interested in ridge functions from the point of view of approximation theory. The basic goal in approximation theory is to approximate complicated objects by simpler objects. Among many classes of multivariate functions, linear combinations of ridge functions are a class of simpler functions. These notes study some problems of approximation of multivariate functions by linear combinations of ridge functions. We present here various properties of these functions. The questions we ask are as follows. When can a multivariate function be expressed as a linear combination of ridge functions from a certain class? When do such linear combinations represent each multivariate function? If a precise representation is not possible, can one approximate arbitrarily well? If well approximation fails, how can one compute/estimate the error of approximation, know that a best approximation exists? How can one characterize and construct best approximations? If a smooth function is a sum of arbitrarily behaved ridge functions, can it be expressed as a sum of smooth ridge functions? We also study properties of generalized ridge functions, which are very much related to linear superpositions and Kolmogorov's famous superposition theorem. These notes end with a few applications of ridge functions to the problem of approximation by single and two hidden layer neural networks with a restricted set of weights. \u0000We hope that these notes will be useful and interesting to both researchers and students.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122192636","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: 5
On a Transform for Modeling Skewness 关于偏度建模的变换
Mathematics eJournal Pub Date : 2020-05-10 DOI: 10.2139/ssrn.3598275
L. Kang, P. Damien, S. Walker
{"title":"On a Transform for Modeling Skewness","authors":"L. Kang, P. Damien, S. Walker","doi":"10.2139/ssrn.3598275","DOIUrl":"https://doi.org/10.2139/ssrn.3598275","url":null,"abstract":"In many applications, data exhibit skewness and in this paper we present a new family of density functions modeling skewness based on a transformation, analagous to those of location and scale. Here we note that location will always refer to mode. Hence, in order to model data to include shape, we need only to find a family of densities exhibiting a variety of shapes, since we can obtain the other three properties via the transformations. The chosen class of densities with the variety of shape is, we argue, the simplest available. Illustrations including regression and time series models are given.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130964192","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: 3
Binned Scatterplots: A Simple Tool to Make Research Easier and Better 分形散点图:一个简单的工具，使研究更容易和更好
Mathematics eJournal Pub Date : 2020-04-12 DOI: 10.2139/ssrn.3257345
Evan Starr, Brent D. Goldfarb
{"title":"Binned Scatterplots: A Simple Tool to Make Research Easier and Better","authors":"Evan Starr, Brent D. Goldfarb","doi":"10.2139/ssrn.3257345","DOIUrl":"https://doi.org/10.2139/ssrn.3257345","url":null,"abstract":"We seek to diffuse a graphical tool—binned scatterplots—which we argue can dramatically improve the quality and speed of research in strategic management. In contrast to the current practice of showing plots of predicted values, binned scatterplots graph the non-parametric relationship between two variables, either unconditionally or conditional on a set of controls, for multiple subgroups. This allows researchers to quickly detect the shape of that relationship, examine outliers, and assess which part of the support may be driving a relationship. We propose that the adoption of binned scatterplots will lead to the identification of new and interesting phenomena, raise the credibility of empirical research, and help create richer theories.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122439683","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: 33
Energy-Frequency Spectrum for Financial Time Series via Complementary Ensemble EMD 基于互补集成EMD的金融时间序列能量频谱
Mathematics eJournal Pub Date : 2020-04-11 DOI: 10.2139/ssrn.3573243
Tim Leung, Theodore Zhao
{"title":"Energy-Frequency Spectrum for Financial Time Series via Complementary Ensemble EMD","authors":"Tim Leung, Theodore Zhao","doi":"10.2139/ssrn.3573243","DOIUrl":"https://doi.org/10.2139/ssrn.3573243","url":null,"abstract":"We discuss the method of complementary ensemble empirical mode decomposition (CEEMD) for analyzing nonstationary financial time series. This noise-assisted approach decomposes any time series into a number of intrinsic mode functions, along with the corresponding instantaneous amplitudes and instantaneous frequencies. Different combinations of modes allows us to reconstruct the time series based on different timescales. Using Hilbert spectral analysis, we compute the associated instantaneous energy-frequency spectrum to illustrate and interpret the properties of various timescales embedded in the original time series.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122165197","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 Regularization Approach for Stable Estimation of Loss Development Factors 损失发展因子稳定估计的一种正则化方法
Mathematics eJournal Pub Date : 2020-04-07 DOI: 10.2139/ssrn.3570959
Himchan Jeong, Hyunwoong Chang, Emiliano A. Valdez
{"title":"A Regularization Approach for Stable Estimation of Loss Development Factors","authors":"Himchan Jeong, Hyunwoong Chang, Emiliano A. Valdez","doi":"10.2139/ssrn.3570959","DOIUrl":"https://doi.org/10.2139/ssrn.3570959","url":null,"abstract":"In this article, we show that a new penalty function, which we call log-adjusted absolute deviation (LAAD), emerges if we theoretically extend the Bayesian LASSO using conjugate hyperprior distributional assumptions. We further show that the estimator with LAAD penalty has closed-form in the case with a single covariate and it can be extended to general cases when combined with coordinate descent algorithm with assurance of convergence under mild conditions. This has the advantages of avoiding unnecessary model bias as well as allowing variable selection, which is linked to the choice of tail factor in loss development for claims reserving. We calibrate our proposed model using a multi-line insurance dataset from a property and casualty company where we observe reported aggregate loss along the accident years and development periods.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127108276","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
Handbook of Financial Risk Management - Companion Book 金融风险管理手册-配套书
Mathematics eJournal Pub Date : 2020-04-01 DOI: 10.2139/ssrn.3638907
T. Roncalli
{"title":"Handbook of Financial Risk Management - Companion Book","authors":"T. Roncalli","doi":"10.2139/ssrn.3638907","DOIUrl":"https://doi.org/10.2139/ssrn.3638907","url":null,"abstract":"This companion book contains the solutions of the tutorial exercises which are included in the Handbook of Financial Risk Management.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122909353","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: 1
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