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引发攀比的比较：作为复合决策的排名与选择AI 解读

There is an innate human tendency, one might call it the “league table mentality,” to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi‐dimensionality would suggest that—at best—only partial orderings were possible. We consider a large class of elementary ranking problems in which we observe noisy, scalar measurements of merit for n objects of potentially heterogeneous precision and are asked to…

随机系数二元响应模型的非参数极大似然方法AI 解读

The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the nonparametric maximum likelihood estimator (NPMLE) of Kiefer and Wolfowitz plays a central role in recent developments of empirical Bayes methods. The NPMLE has also been proposed by Cosslett as an estimation method for single index linear models for binary response with random coefficients.…

含治愈比例的删失生存分位数回归模型AI 解读

A new quantile regression model for survival data is proposed that permits a positive proportion of subjects to become unsusceptible to recurrence of disease following treatment or based on other observable characteristics. In contrast to prior proposals for quantile regression estimation of censored survival models, we propose a new “data augmentation” approach to estimation. Our approach has computational advantages over earlier approaches proposed by Wu and Yin (2013,…

混合模型中的同质性检验AI 解读

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C ( α ) tests, as in Neyman (1959), and shown to be locally asymptotically optimal. These C ( α ) tests will be contrasted with a new approach to likelihood ratio testing for general mixture models. The latter tests are based…

经验贝叶斯棒球再论：纵向数据的经验贝叶斯方法AI 解读

Summary Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A recent convex optimization reformulation of the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz ( Annals of Mathematical Statistics 1956; 27 : 887–906) is employed to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with an application to predict baseball batting averages, and the age…

收入动态中的未观测异质性：经验贝叶斯视角AI 解读

Empirical Bayes methods for Gaussian compound decision problems involving longitudinal data are considered. The new convex optimization formulation of the nonparametric (Kiefer–Wolfowitz) maximum likelihood estimator for mixture models is employed to construct nonparametric Bayes rules for compound decisions. The methods are first illustrated with some simulation examples and then with an application to models of income dynamics. Using panel data, we estimate a simple…

凸优化、形状约束、复合决策与经验贝叶斯规则AI 解读

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Jiang and Zhang, proposes a new approach to computing the Kiefer–Wolfowitz nonparametric…

拟凹密度估计AI 解读

Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. A…

疯狂三月、分位数回归对阵预测与哈耶克假说AI 解读

A quantile regression variant of the classical paired comparison model of mean ratings is proposed. The model is estimated using data for the regular 2004–2005 U.S. college basketball season, and evaluated based on predictive performance for the 2005 National Collegiate Athletic Association (NCAA) basketball tournament. Rather than basing predictions entirely on conditional mean estimates produced by classical least-squares paired comparison methods, the proposed methods…

GARCH 模型的条件分位数估计AI 解读

Conditional quantile estimation is an essential ingredient in modern risk management. Although generalized autoregressive conditional heteroscedasticity (GARCH) processes have proven highly successful in modeling financial data, it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this article we study estimation of…

二元选择模型的参数化链接函数：频率学派与贝叶斯的对话AI 解读

The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey [lambda] family, with two shape parameters controlling…

论可复现的计量经济学研究AI 解读

Abstract Recent software developments are reviewed from the vantage point of reproducible econometric research. We argue that the emergence of new tools, particularly in the open‐source community, have greatly eased the burden of documenting and archiving both empirical and simulation work in econometrics. Some of these tools are highlighted in the discussion of two small replication exercises. Copyright © 2009 John Wiley & Sons, Ltd.

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分位数自回归AI 解读

We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale, and shape of the conditional distribution of the response, and thus constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a…

单位根分位数自回归推断AI 解读

We study statistical inference in quantile autoregression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey–Fuller distribution, but rather a linear combination of the Dickey–Fuller distribution and the standard normal, with the weight determined by the correlation coefficient of related time series.…

惩罚三角网模型：二维平滑的全变差正则化AI 解读

Summary Hansen, Kooperberg and Sardy introduced a family of continuous, piecewise linear functions defined over adaptively selected triangulations of the plane as a general approach to statistical modelling of bivariate densities and regression and hazard functions. These triograms enjoy a natural affine equivariance that offers distinct advantages over competing tensor product methods that are more commonly used in statistical applications. Triograms employ basis functions…

分位数回归过程的统计推断AI 解读

Abstract. Tests based on the quantile regression process can be formulated like the classical Kolmogorov-Smirnov and Cramer-von-Mises tests of goodness-of-t employing the theory of Bessel processes as in Kiefer (1959). However, it is fre-quently desirable to formulate hypotheses involving unknown nuisance parameters, thereby jeopardizing the distribution free character of these tests. We characterize this situation as \\the Durbin problem " since it was posed in Durbin…

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分位数回归的拟合优度及相关推断过程AI 解读

We introduce a goodness-of-fit process for quantile regression analogous to the conventional R2 statistic of least squares regression. Several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier p-sample goodness-of-fit theory involving Bessel…

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ARCH 模型的条件分位数估计与推断AI 解读

Quantile regression methods are suggested for a class of ARCH models. Because conditional quantiles are readily interpretable in semiparametric ARCH models and are inherendy easier to estimate robustly than population moments, they offer some advantages over more familiar methods based on Gaussian likelihoods. Related inference methods, including the construction of prediction intervals, are also briefly discussed.

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矩展开与最小距离估计的稳健性AI 解读

This paper explores the robustness of minimum distance (GMM) estimators focusing particularly on the effect of intermediate covariance matrix estimation on final estimator performance. Asymptotic expansions to order O p ( n −3/2 ) are employed to construct O ( n −2 ) expansions for the variance of estimators constructed from preliminary least-squares and general M -estimators. In the former case, there is a rather curious robustifying effect due to estimation of the…

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