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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,…

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…

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…

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…

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…

条件分位数的层级样条模型与电力需求AI 解读

Methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of Koenker and Bassett. Spline parameterizations of the conditional quantile functions are used. The methods are illustrated by estimating hierarchical models for household electricity demand using data from the Chicago metropolitan area. The empirical results show that lower quantiles of demand (“base-load”) vary only slightly across residential…

线性模型的自适应 L 估计AI 解读

Asymptotically efficient (adaptive) estimators for the slope parameters of the linear regression model are constructed based upon the "regression quantile" statistics suggested by Koenker and Bassett. The estimators are natural analogues of the adaptive $L$-estimators of location of Sacks, but employ kernel-density type estimators of the optimal $L$-estimator weight function.

线性模型的 L 估计AI 解读

Linear combinations of order statistics, or L-estimators, have played an extremely important role in the development of robust methods for the one-sample problem. We suggest analogs of L-estimators for the parameters of the linear model based on the p-dimensional “regression quantiles” proposed by Koenker and Bassett (1978). A uniform, Bahadur-type asymptotic representation of regression quantiles is established, and this yields a general asymptotic theory of L-estimators…

独立同分布误差线性模型的经验分位数函数AI 解读

The regression quantile statistics of Koenker and Bassett (1978) are employed to construct an estimate of the error quantile function in linear models with iid errors. Some finite sample properties and the asymptotic behavior of the proposed estimator are derived. Comparisons with procedures based on residuals are made. The stackloss data of Brownlee (1965) is reanalyzed to illustrate the technique

最小绝对误差回归的渐近理论AI 解读

In the general linear model with independent and identically distributed errors and distribution function F, the estimator which minimizes the sum of absolute residuals is demonstrated to be consistent and asymptotically Gaussian with covariance matrix ω2 Q -1, where Q = lim T -1 X'X and ω2 is the asymptotic variance of the ordinary sample median from samples with distribution F. Thus the least absolute error estimator has strictly smaller asymptotic confidence ellipsoids…

回归分位数AI 解读

A simple minimization problem yielding the ordinary sample quantiles in the location model is shown to generalize naturally to the linear model generating a new class of statistics we term “regression quantiles.” The estimator which minimizes the sum of absolute residuals is an important special case. Some equivariance properties and the joint asymptotic distribution of regression quantiles are established. These results permit a natural generalization to the linear model of…