Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, including Markovian property, hidden Markovian structure, contaminated observations, and random samples. We then discuss several popular parametric and nonparametric estimation methods. To avoid model mis-specification, model validation plays a key role in financial modeling. We discuss several model validation techniques, including pseudo-likelihood ratio test, nonparametric curve regression based test, residuals based test, generalized likelihood ratio test, simultaneous confidence band construction, and density based test. Finally, we briefly touch on tools for studying large sample properties.
{"title":"Parametric and nonparametric models and methods in financial econometrics","authors":"Zhibiao Zhao","doi":"10.1214/08-SS034","DOIUrl":"https://doi.org/10.1214/08-SS034","url":null,"abstract":"Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, including Markovian property, hidden Markovian structure, contaminated observations, and random samples. We then discuss several popular parametric and nonparametric estimation methods. To avoid model mis-specification, model validation plays a key role in financial modeling. We discuss several model validation techniques, including pseudo-likelihood ratio test, nonparametric curve regression based test, residuals based test, generalized likelihood ratio test, simultaneous confidence band construction, and density based test. Finally, we briefly touch on tools for studying large sample properties.","PeriodicalId":46627,"journal":{"name":"Statistics Surveys","volume":"16 1","pages":"1-42"},"PeriodicalIF":3.3,"publicationDate":"2008-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74426773","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}
An important feature of linear mixed models and generalized linear mixed models is that the conditional mean of the response given the random effects, after transformed by a link function, is linearly related to the fixed covariate effects and random effects. Therefore, it is of practical importance to test the adequacy of this assumption, particularly the assumption of linear covariate effects. In this paper, we review procedures that can be used for testing polynomial covariate effects in these popular models. Specifically, four types of hypothesis testing approaches are reviewed, i.e. R tests, likelihood ratio tests, score tests and residual-based tests. Derivation and performance of each testing procedure will be discussed, including a small simulation study for comparing the likelihood ratio tests with the score tests.
{"title":"Testing polynomial covariate effects in linear and generalized linear mixed models.","authors":"Mingyan Huang, Daowen Zhang","doi":"10.1214/08-ss036","DOIUrl":"https://doi.org/10.1214/08-ss036","url":null,"abstract":"<p><p>An important feature of linear mixed models and generalized linear mixed models is that the conditional mean of the response given the random effects, after transformed by a link function, is linearly related to the fixed covariate effects and random effects. Therefore, it is of practical importance to test the adequacy of this assumption, particularly the assumption of linear covariate effects. In this paper, we review procedures that can be used for testing polynomial covariate effects in these popular models. Specifically, four types of hypothesis testing approaches are reviewed, i.e. R tests, likelihood ratio tests, score tests and residual-based tests. Derivation and performance of each testing procedure will be discussed, including a small simulation study for comparing the likelihood ratio tests with the score tests.</p>","PeriodicalId":46627,"journal":{"name":"Statistics Surveys","volume":"2 ","pages":"154-169"},"PeriodicalIF":3.3,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/08-ss036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"28428320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in wavelet applications to statistics and to the analysis of experimental data, with many successes in the efficient analysis, processing, and compression of noisy signals and images. This is a selective review article that attempts to synthesize some recent work on ``nonlinear'' wavelet methods in nonparametric curve estimation and their role on a variety of applications. After a short introduction to wavelet theory, we discuss in detail several wavelet shrinkage and wavelet thresholding estimators, scattered in the literature and developed, under more or less standard settings, for density estimation from i.i.d. observations or to denoise data modeled as observations of a signal with additive noise. Most of these methods are fitted into the general concept of regularization with appropriately chosen penalty functions. A narrow range of applications in major areas of statistics is also discussed such as partial linear regression models and functional index models. The usefulness of all these methods are illustrated by means of simulations and practical examples.
{"title":"Wavelet methods in statistics: Some recent developments and their applications","authors":"A. Antoniadis","doi":"10.1214/07-SS014","DOIUrl":"https://doi.org/10.1214/07-SS014","url":null,"abstract":"The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in wavelet applications to statistics and to the analysis of experimental data, with many successes in the efficient analysis, processing, and compression of noisy signals and images. This is a selective review article that attempts to synthesize some recent work on ``nonlinear'' wavelet methods in nonparametric curve estimation and their role on a variety of applications. After a short introduction to wavelet theory, we discuss in detail several wavelet shrinkage and wavelet thresholding estimators, scattered in the literature and developed, under more or less standard settings, for density estimation from i.i.d. observations or to denoise data modeled as observations of a signal with additive noise. Most of these methods are fitted into the general concept of regularization with appropriately chosen penalty functions. A narrow range of applications in major areas of statistics is also discussed such as partial linear regression models and functional index models. The usefulness of all these methods are illustrated by means of simulations and practical examples.","PeriodicalId":46627,"journal":{"name":"Statistics Surveys","volume":"74 1","pages":"16-55"},"PeriodicalIF":3.3,"publicationDate":"2007-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86166282","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}
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data, but this is complicated by the lack of formal probabilistic models for packings. Without formal models, simulation algorithms and collections of physical objects must be used as models. Identification of common aspects of different realizations of the same packing process requires the use of new descriptive statistics, many of which have yet to be developed. Model assessment will require the use of large samples of independent and identically distributed realizations, rather than the large single stationary realizations found in conventional spatial statistics. The development of procedures for model assessment will resemble the development of thermodynamic models, and will be based on much exploration and experimentation rather than on extensions of established statistical methods.
{"title":"Statistical inference for disordered sphere packings","authors":"J. Picka","doi":"10.1214/09-SS058","DOIUrl":"https://doi.org/10.1214/09-SS058","url":null,"abstract":"Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data, but this is complicated by the lack of formal probabilistic models for packings. Without formal models, simulation algorithms and collections of physical objects must be used as models. Identification of common aspects of different realizations of the same packing process requires the use of new descriptive statistics, many of which have yet to be developed. Model assessment will require the use of large samples of independent and identically distributed realizations, rather than the large single stationary realizations found in conventional spatial statistics. The development of procedures for model assessment will resemble the development of thermodynamic models, and will be based on much exploration and experimentation rather than on extensions of established statistical methods.","PeriodicalId":46627,"journal":{"name":"Statistics Surveys","volume":"50 1","pages":"74-112"},"PeriodicalIF":3.3,"publicationDate":"2007-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79942200","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}
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