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Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.


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TL;DR: In this paper, the identification and estimation of hedonic models is studied in an additive version of the model, where technology and preferences are identified up to affine transformations from data on demand and supply in a single market.
Abstract: This paper considers the identification and estimation of hedonic models. We establish that in an additive version of the hedonic model, technology and preferences are generically identified up to affine transformations from data on demand and supply in a single hedonic market. For a very general parametric structure, preferences and technology are fully identified. This is true under a strong assumption of statistical independence of the error term. It is also true under the weaker assumption of mean independence of the error term. Much of the confusion in the empirical literature that claims that hedonic models estimated on data from a single market are fundamentally underidentified is based on linearizations that do not use all of the information in the model. The exact economic model that justifies widely used linear approximations has strange properties so the approximation is doubly poor. A semiparametric estimation method is proposed that is valid when a statistical independence assumption is valid. Alternatively, under the weaker condition of mean independence instrumental variables estimators can be applied to identify technology and preference parameters from a single market. They are justified by nonlinearities that are generic features of equilibrium in hedonic models.

502 citations

Journal ArticleDOI
TL;DR: Adaptive branch-site random effects likelihood (aBSREL), whose key innovation is variable parametric complexity chosen with an information theoretic criterion, delivers statistical performance matching or exceeding best-in-class existing approaches, while running an order of magnitude faster.
Abstract: Over the past two decades, comparative sequence analysis using codon-substitution models has been honed into a powerful and popular approach for detecting signatures of natural selection from molecular data. A substantial body of work has focused on developing a class of “branch-site” models which permit selective pressures on sequences, quantified by the ω ratio, to vary among both codon sites and individual branches in the phylogeny. We develop and present a method in this class, adaptive branch-site random effects likelihood (aBSREL), whose key innovation is variable parametric complexity chosen with an information theoretic criterion. By applying models of different complexity to different branches in the phylogeny, aBSREL delivers statistical performance matching or exceeding best-in-class existing approaches, while running an order of magnitude faster. Based on simulated data analysis, we offer guidelines for what extent and strength of diversifying positive selection can be detected reliably and suggest that there is a natural limit on the optimal parametric complexity for “branch-site” models. An aBSREL analysis of 8,893 Euteleostomes gene alignments demonstrates that over 80% of branches in typical gene phylogenies can be adequately modeled with a single ω ratio model, that is, current models are unnecessarily complicated. However, there are a relatively small number of key branches, whose identities are derived from the data using a model selection procedure, for which it is essential to accurately model evolutionary complexity.

501 citations

Posted Content
TL;DR: In this paper, a general time inhomogeneous multiple spell model is presented, which contains a variety of useful models as special cases, and conditions under which access to multiple spell data aids in solving the sensitivity problem.
Abstract: This paper considers the formulation and estimation of continuous time social science duration models. The focus is on new issues that arise in applying statistical models developed in biostatistics to analyze economic data and formulate economic models. Both single spell and multiple spell models are discussed. In addition, we present a general time inhomogeneous multiple spell model which contains a variety of useful models as special cases.Four distinctive features of social science duration analysis are emphasized:(1) Because of the limited size of samples available in economics and because of an abundance of candidate observed explanatory variables and plausible omitted explanatory variables, standard nonparametric procedures used in biostatistics are of limited value in econometric duration analysis. It is necessary to control for observed and unobserved explanatory variables to avoid biasing inference about underlying duration distributions. Controlling for such variables raises many new problems not discussed in the available literature.(2) The environments in which economic agents operate are not the time homogeneous laboratory environments assumed in biostatistics and reliability theory. Ad hoc methods for controlling for time inhomogeneity produce badly biased estimates.(3) Because the data available to economists are not obtained from the controlled experimental settings available to biologists, doing econometric duration analysis requires accounting for the effect of sampling plans on the distributions of sampled spells.(4) Econometric duration models that incorporate the restrictions produced by economic theory only rarely can be represented by the models used by biostatisticians. The estimation of structural econometric duration models raises new statistical and computational issues.Because of (1) it is necessary to parameterize econometric duration models to control for both observed and unobserved explanatory variables. Economic theory only provides qualitative guidance on the matter of selecting a functional form for a conditional hazard, and it offers no guidance at all on the matter of choosing a distribution of unobservables. This is unfortunate because empirical estimates obtained from econometric duration models are very sensitive to assumptions made about the functional forms of these model ingredients.In response to this sensitivity we present criteria for inferring qualitative properties of conditional hazards and distributions of unobservables from raw duration data sampled in time homogeneous environments; i.e. from unconditional duration distributions. No parametric structure need be assumed to implement these procedures.We also note that current econometric practice overparameterizes duration models. Given a functional form for a conditional hazard determined up to a finite number of parameters, it is possible to consistently estimate the distribution of unobservables nonparametrically. We report on the performance of such an estimator and show that it helps to solve the sensitivity problem.We demonstrate that in principle it is possible to identify both the conditional hazard and the distribution of unobservables without assuming parametric functional forms for either. Tradeoffs in assumptions required to secure such model identification are discussed. Although under certain conditions a fully nonparametric model can be identified, the development of a consistent fully nonparametric estimator remains to be done.We also discuss conditions under which access to multiple spell data aids in solving the sensitivity problem. A superficially attractive conditional likelihood approach produces inconsistent estimators, but the practical significance of this inconsistency is not yet known. Conditional inference schemes for eliminating unobservables from multiple spell duration models that are based on sufficient or ancillary statistics require unacceptably strong assumptions about the functional forms of conditional hazards and so are not robust. Contrary to recent claims, they offer no general solution to the model sensitivity problem.The problem of controlling for time inhomogeneous environments (Point (2)) remains to be solved. Failure to control for time inhomogeneity produces serious biases in estimated duration models. Controlling for time inhomogeneity creates a potential identification problem.For a single spell data it is impossible to separate the effect of duration dependence from the effect of time inhomogeneity by a fully nonparametric procedure. Although it is intuitively obvious that access to multiple spell data aids in the solution of this identification problem, the development of precise conditions under which this is possible is a topic left for future research.We demonstrate how sampling schemes distort the functional forms of sample duration distributions away from the population duration distributions that are the usual object of econometric interest (Point (3)). Inference based on misspecified duration distributions is in general biased. New formulae for the densities of commonly used duration measures are produced for duration models with unobservables in time inhomogeneous environments. We show how access to spells that begin after the origin date of a sample aids in solving econometric problems created by the sampling schemes that are used to generate economic duration data.We also discuss new issues that arise in estimating duration models explicitly derived from economic theory (Point (4)). For a prototypical search unemployment model we discuss and resolve new identification problems that arise in attempting to recover structural economic parameters. We also consider nonstandard statistical problems that arise in estimating structural models that are not treated in the literature. Imposing or testing the restrictions implied by economic theory requires duration models that do not appear in the received literature and often requires numerical solution of implicit equations derived from optimizing theory.

500 citations

Journal ArticleDOI
TL;DR: In this article, the theory of the three-wave parametric instability for weakly inhomogeneous media is derived with an application to laser pellet irradiation and applied to laser beamforming.
Abstract: The theory of the three-wave parametric instability for weakly inhomogeneous media is derived with an application to laser pellet irradiation.

496 citations

Book
15 Dec 1995
TL;DR: In this paper, the authors present an approach for regression analysis based on univariate and univariate descriptive statistics and nonparametric statistics, as well as regression analysis for time series models.
Abstract: 1. Statistics and Geography I. Descriptive Statistics 2. Univariate Descriptive Statistics 3. Descriptive Statistics for Spatial Distributions II. Inferential Statistics 5. Elementary Probability Theory 6. Random Variables and Probability Distributions 7. Sampling 8. Parametric Statistical Inference: Estimation 9. Parametric Statistical Inference: Hypothesis Testing 10. Parametric Statistical Inference: Two Sample Tests 11. Nonparametric Statistics III. Statistical Relationships Between Two Variables 12. Correlation Analysis 13. Introduction to Regression Analysis 14. Inferential Aspects of Regression Analysis 15. Time Series Models IV. Modern Methods of Analysis 16. Exploratory Data Analysis 17. Bootstrapping and Related Computer Intensive Methods

493 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20252
20242
20233,966
20227,822
20211,968
20202,033