Oracle Inequalities for Convex Loss Functions with Nonlinear Targets

This article considers penalized empirical loss minimization of convex loss functions with unknown target functions. Using the elastic net penalty, of which the Least Absolute Shrinkage and Selection Operator (Lasso) is a special case, we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear, this inequality also provides an upper bound of the estimation error of the estimated parameter vector. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear, we give sufficient conditions for consistency of the estimated parameter vector. We briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions covered by our framework.     

Temporal Disaggregation: Methods,Information Loss,and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.     

Bayesian estimation and influence diagnostics of generalized partially linear mixed-effects models for longitudinal data

This paper develops a Bayesian approach to obtain the joint estimates of unknown parameters, nonparametric functions and random effects in generalized partially linear mixed models (GPLMMs), and presents three case deletion influence measures to identify influential observations based on the φ-divergence, Cook's posterior mean distance and Cook's posterior mode distance of parameters. Fisher's iterative scoring algorithm is developed to evaluate the posterior modes of parameters in GPLMMs. The first-order approximation to Cook's posterior mode distance is presented. The computationally feasible formulae for the φ-divergence diagnostic and Cook's posterior mean distance are given. Several simulation studies and an example are presented to illustrate our proposed methodologies.     

曲线分类建模方法及其在GDP预测中的应用

传统方法解决大规模时序曲线的预测建模问题,需要对每条曲线逐一建模,使得建模工作量相当庞大,在实际应用中缺乏可操作性。文章提出一种解决此问题的新方法——曲线分类建模方法。该方法先减少曲线的模型种类,再进行曲线分类和分类建模,在尽可能保留原始信息的前提下较大程度地降低了建模的工作量。文章阐述了该方法的原理和计算过程,并以应用于多地区GDP曲线的预测案例说明该方法的实用性和有效性。     

侵权法中的机会丧失理论

机会丧失理论即加害人的加害行为导致受害人获得利益或避免损害的机会丧失时,加害人应对此种机会的丧失承担损害赔偿责任的学说。它是对传统侵权法理论的修正和补充,并对损害、因果关系等侵权构成要件的传统学说造成了一定冲击。该理论在英美法系国家以及德国、法国等国的司法实践中多有运用,但关于其适用及其适用范围尚存诸多争议。我国机会丧失案件并不少见,但却没有采纳机会丧失理论。本文在介绍机会丧失理论的内涵及各国发展状况的基础上,着重探讨它在侵权法上适用的法律和政策方面的主要争议,并提出可供我国司法实践借鉴的建议。     

对国有资产中有形资产流失问题的探讨

国有资产中有形资产的流失存在动态流失与静态流失两种形式,动态流失因产权不清、管理不严或产权交易中规则不健全所致,具体又可分为经营性动态流失和人为性动态流失．静态流失与其是否进入市场交易有关．加强经济立法,完善和发展产权交易市场等可减少或避免国有有形资产的流失。     

Correlation in a Bayesian framework

The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.     

Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

On predictive distributions and Bayesian networks

In this paper we are interested in discrete prediction problems for a decision-theoretic setting, where the task is to compute the predictive distribution for a finite set of possible alternatives. This question is first addressed in a general Bayesian framework, where we consider a set of probability distributions defined by some parametric model class. Given a prior distribution on the model parameters and a set of sample data, one possible approach for determining a predictive distribution is to fix the parameters to the instantiation with the maximum a posteriori probability. A more accurate predictive distribution can be obtained by computing the evidence (marginal likelihood), i.e., the integral over all the individual parameter instantiations. As an alternative to these two approaches, we demonstrate how to use Rissanen's new definition of stochastic complexity for determining predictive distributions, and show how the evidence predictive distribution with Jeffrey's prior approaches the new stochastic complexity predictive distribution in the limit with increasing amount of sample data. To compare the alternative approaches in practice, each of the predictive distributions discussed is instantiated in the Bayesian network model family case. In particular, to determine Jeffrey's prior for this model family, we show how to compute the (expected) Fisher information matrix for a fixed but arbitrary Bayesian network structure. In the empirical part of the paper the predictive distributions are compared by using the simple tree-structured Naive Bayes model, which is used in the experiments for computational reasons. The experimentation with several public domain classification datasets suggest that the evidence approach produces the most accurate predictions in the log-score sense. The evidence-based methods are also quite robust in the sense that they predict surprisingly well even when only a small fraction of the full training set is used.