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ESTIMATING EULER EQUATIONS WITH NOISY DATA: TWO EXACT GMM ESTIMATORS

JOURNAL OF APPLIED ECONOMETRICS 2009年第2期24卷 309-324页

作者： Alan, Sule Attanasio, Orazio Browning, Martin Univ Cambridge Fac Econ Cambridge England UCL Dept Econ London England Univ Oxford Dept Econ Oxford England

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is log-normally distributed. The second estimator drops the distributional assumption at the cost of less precision. Our Monte Carlo results suggest that both proposed estimators perform Much better than conventional alternatives based on the exact Euler equation or its log-linear approximation, especially with short panels. An empirical application to the PSID yields plausible and precise estimates of the coefficient of relative risk aversion and the discount rate. Copyright (C) 2008 John Wiley & Sons. Ltd.

关键词： MONTE Carlo method REGRESSION analysis RISK aversion UTILITY theory EQUATIONS log-linear models MEASUREMENT errors

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Temporal Patterns of Variable Relationships in Person-Oriented Research: Prediction and Auto-Association models of Configural Frequency Analysis

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APPLIED DEVELOPMENTAL SCIENCE 2009年第4期13卷 172-187页

作者： von Eye, Alexander Mun, Eun Young Bogat, G. Anne Michigan State Univ E Lansing MI 48824 USA Rutgers State Univ Piscataway NJ 08855 USA

Longitudinal Configural Frequency Analysis (CFA) seeks to identify, at the manifest variable level, those temporal patterns that are observed more frequently (CFA types) or less frequently (CFA antitypes) than expected with reference to a base model. This article discusses, compares, and extends two base models of interest in longitudinal data analysis. The first of these, Prediction CFA (P-CFA), is a base model that can be used in the configural analysis of both cross-sectional and longitudinal data. This model takes the associations among predictors and among criteria into account. The second base model, Auto-Association CFA (A-CFA), was specifically designed for longitudinal data. This model takes the auto-associations among repeatedly observed variables into account. Both models are extended to accommodate covariates, for example, stratification variables. Application examples are given using data from a longitudinal study of domestic violence. It is illustrated that CFA is able to yield results that are not redundant with results from log-linear modeling or multinomial regression. It is concluded that CFA is particularly useful in the context of person-oriented research.

关键词： REGRESSION analysis DATA analysis ALGORITHMS MANAGEMENT science FREQUENCIES of oscillating systems LONGITUDINAL method FAMILY violence log-linear models STATISTICAL power analysis

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Population Size Estimation Using Individual Level Mixture models

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BIOMETRICAL JOURNAL 2008年第6期50卷 1051-1063页

作者： Manrique-Vallier, Daniel Fienberg, Stephen E. Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA Carnegie Mellon Univ Machine Learning Dept Pittsburgh PA 15213 USA

We revisit the heterogeneous closed Population multiple recapture problem, modeling individual-level heterogeneity using the Grade of Membership model (Woodbury et al., 1978). This strategy allows us to postulate the existence of homogeneous latent "ideal" or "pure" classes within the population, and construct a soft clustering of the individuals, where each one is allowed partial or mixed membership in all of these classes. We propose a full hierarchical Bayes specification and a MCMC algorithm to obtain samples from the posterior distribution. We apply the method to Simulated data and to three real life examples.

关键词： Capture-recapture Dependence Grade of Membership models Heterogeneity Hierarchical Bayes BIC log-linear models Rasch model

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Increasing perfluoroalkyl contaminants in east Greenland polar bears (Ursus maritimus):: A new toxic threat to the Arctic bears

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ENVIRONMENTAL SCIENCE & TECHNOlogY 2008年第7期42卷 2701-2707页

作者： Dietz, R. Bossi, R. Riget, F. F. Sonne, C. Born, E. W. Univ Aarhus Natl Environm Res Inst Dept Arctic Environm DK-4000 Roskilde Denmark Univ Aarhus Natl Environm Res Inst Dept Atmospher Environm DK-4000 Roskilde Denmark Greenland Inst Nat Resources DK-3900 Nuuk Greenland

A well-defined subsample of 128 subadult (3-5 years) polar bears (Ursus maritimus) from 19 sampling years within the period 1984-2006 was investigated for perfluoroalkyl contaminants (PFCs), linear regression analysis of logarithmic-transformed median concentrations showed significant annual increases for PFOS (4.7%), PFNA (6.1%), PFUnA (5.9%), PFDA (4.3%), PFTrA (8.5%), PFOA (2.3%), and PFDoA (5.2%). For four of the PFCs, a LOESS smoother model provided significantly better descriptions, revealing steeper linear annual increases for PFOSA of 9.2% after 1990 and between 18.6 and 27.4% for PFOS, PFDA, and PFTrA after 2000. Concentrations of Sigma PFCs, by 2006, exceeded the concentrations of all conventional OHCs (organohalogen compounds), of which several have been documented to correlate with a number of negative health effects. If the PFC concentrations in polar bears continue to increase with the steepest observed trends, then the lowest no-adverse-effect level (NOAEL) and lowest-adverse-effect level (LOAEL) detected for rats and monkeys will be exceeded in 2014-2024. In addition, the rapidly increasing concentrations of PFCs are likely to cause cumulative and combined effects on the polar bear, compounding the already detected threats from OHCs.

关键词： Regression analysis Pollution Polar bear Organic compounds Organohalogen compounds logarithmic functions Perfluorocarbons log-linear models

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On imputing continuous data when the eventual interest pertains to ordinalized outcomes via threshold concept

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2008年第4期52卷 2261-2271页

作者： Demirtas, Hakan Univ Illinois Div Epidemiol & Biostat Chicago IL 60612 USA

Multiple imputation under the multivariate normality assumption has often been considered a workable model-based approach in dealing with incomplete continuous data. A situation where the measurements are taken on a continuous scale with an eventual interest in ordinalized versions via threshold concept is commonly encountered in applied research, especially in medical and social sciences. In practice, researchers ordinarily impute missing values for continuous outcomes under a Gaussian imputation model, and then ordinalize them via pre-specified cutoff points. An alternate strategy is creating multiply imputed data sets after ordinalization under a log-linear imputation model that uses a saturated multinomial structure. In this work, the performances of the two imputation methods were examined on a fairly broad range of simulated incomplete data sets that exhibit varying distributional characteristics such as skewness and multimodality. Behavior of efficiency and accuracy measures was investigated to determine the degree to which the procedures work appositely. The conclusion drawn is that ordinalization before carrying out a log-linear imputation should be the preferred procedure except for a few special cases. It is recommended that researchers use the less common second strategy whenever the interest centers on ordinal quantities that are obtained through underlying continuous measurements. This postulate is probably due to the transformation of non-Gaussian features into better-behaving categorical trends in this particular missing-data environment. This premise preponderates the factual argument that continuous variables intrinsically convey more information, leading to a counter-intuitive, but potentially beneficial result for practitioners. (c) 2007 Elsevier B.V. All rights reserved.

关键词： multivariate normality multiple imputation log-linear models skewness multimodality

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An application of multinomial logistic regression to estimating performance of a multiple-screening test with incomplete verification

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS 2008年第Pt1期57卷 89-102页

作者： Lloyd, Chris J. Frommer, Donald J. Univ Melbourne Melbourne Business Sch Melbourne Vic 3053 Australia St Vincents Hosp Darlinghurst NSW Australia

The paper describes a method of estimating the performance of a multiple-screening test where those who test negatively do not have their true disease status determined. The methodology is motivated by a data set on 49927 subjects who were given K=6 binary tests for bowel cancer. A complicating factor is that individuals may have polyps in the bowel, a condition that the screening test is not designed to detect but which may be worth diagnosing. The methodology is based on a multinomial logit model for Pr(S vertical bar R-6), the probability distribution of patient status S (healthy, polyps or diseased) conditional on the results R-6 from six binary tests. An advantage of the methodology described is that the modelling is data driven. In particular, we require no assumptions about correlation within subjects, the relative sensitivity of the K tests or the conditional independence of the tests. The model leads to simple estimates of the trade-off between different errors as the number of tests is varied, presented graphically by using receiver operating characteristic curves. Finally, the model allows us to estimate better protocols for assigning subjects to the disease group, as well as the gains in accuracy from these protocols.

关键词： log-linear models partial verification receiver operating characteristic curves

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Symmetric measures via moments

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BERNOULLI 2008年第2期14卷 362-390页

作者： Koloydenko, Alexey Univ Nottingham Div Stat Nottingham NG7 2RD England

Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection, namely, one between probabilistic models invariant under a finite group of (nonsingular) linear transformations and polynomials invariant under the same group. Two specific aspects of the connection are discussed: generalization of the (uniqueness part of the multivariate) problem of moments and log-linear, or toric, modeling by expansion of invariant terms. A distribution of minuscule subimages extracted from a large database of natural images is analyzed to illustrate the above concepts.

关键词： algebraic statistics determinate measures finite groups linear transformations log-linear models maximum entropy polynomial invariants symmetry toric models

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A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

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LIFETIME DATA ANALYSIS 2008年第3期14卷 316-332页

作者： Barros, Michelli Paula, Gilberto A. Leiva, Victor Univ Sao Paulo Dept Stat Sao Paulo Brazil Univ Fed Campina Grande Dept Math & Stat Campina Grande Brazil Univ Valparaiso Dept Stat Valparaiso 5030 Chile

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

关键词： generalized Birnbaum-Saunders distribution likelihood methods local influence log-linear models residual analysis robustness sinh-normal distribution

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Exponentiated Gradient Algorithms for Conditional Random Fields and Max-Margin Markov Networks

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JOURNAL OF MACHINE LEARNING RESEARCH 2008年第8期9卷 1775-1822页

作者： Collins, Michael Globerson, Amir Koo, Terry Carreras, Xavier Bartlett, Peter L. MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA Univ Calif Berkeley Div Comp Sci Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function;the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O (1/epsilon) EG updates are required to reach a given accuracy e in the dual;in contrast, for log-linear models only O (log (1/epsilon)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

关键词： exponentiated gradient log-linear models maximum-margin models structured prediction conditional random fields

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Comparison of ordinary and penalized power-divergence test statistics for small and moderate samples in three-way contingency tables via simulation

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2008年第8期37卷 1593-1602页

作者： Alin, Aylin Dokuz Eylul Univ Fen Edebiyat Fak Istatist Bolumu TR-35160 Izmir Turkey

In this article, size and power properties of the ordinary and penalized power-divergence test statistics have been compared to test a nested sequence of log-linear models for various penalization and lambda values. 2 x 2 x 2 contingency tables distributed according to a multinomial distribution are considered. The simulation study results reveal that the penalized power-divergence test statistics with penalization value of one and lambda = -1.5, -2 are the best choices for small and moderate samples, respectively.

关键词： contingency table log-linear models penalization penalized power-divergence measure power-divergence measure

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