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Estimation and Forecasting in Models with Multiple Breaks

多重结构突变模型的估计与预测

This paper develops a new approach to change-point modelling that allows the number of change-points in the observed sample to be unknown. The model we develop assumes that regime durations have a Poisson distribution. It approximately nests the two most common approaches: the time-varying parameter (TVP) model with a change-point every period and the change-point model with a small number of regimes. We focus considerable attention on the construction of reasonable…

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Coefficient Sign Prediction Methods for Model Selection

基于系数符号预测的模型选择方法

Summary We consider a Bayesian model selection strategy based on predicting the signs of the coefficients in a regression model, i.e. we consider identification of coefficients in a full or encompassing model for which we can confidently predict whether they are positive or negative. This is useful when our main purpose in doing model selection is interpretation, since the sign of a coefficient is often of primary importance for this task. In the case of a linear model with…

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The Optimal Discovery Procedure: A New Approach to Simultaneous Significance Testing

最优发现程序:同时显著性检验的新方法

Summary The Neyman–Pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known. This result has played a major role in the development of significance testing strategies that are used in practice. Most of the work extending single-testing strategies to multiple tests has focused on formulating and estimating new types of significance measures, such as the false discovery rate. These methods tend to…

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Spatial Bayesian Variable Selection With Application to Functional Magnetic Resonance Imaging

空间贝叶斯变量选择及其在功能磁共振成像中的应用

We propose a procedure to undertake Bayesian variable selection and model averaging for a series of regressions located on a lattice. For those regressors that are in common in the regressions, we consider using an Ising prior to smooth spatially the indicator variables representing whether or not the variable is zero or nonzero in each regression. This smooths spatially the probabilities that each independent variable is nonzero in each regression and indirectly smooths…

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Model Averaging and Dimension Selection for the Singular Value Decomposition

奇异值分解的模型平均与维度选择

Many multivariate data-analysis techniques for an m × n matrix Y are related to the model Y = M + E, where Y is an m × n matrix of full rank and M is an unobserved mean matrix of rank K < (m ∧ n). Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this article we suggest a model-based alternative to the preceding…

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A ROBUST BAYESIAN APPROACH FOR UNIT ROOT TESTING

单位根检验的稳健贝叶斯方法

In this paper we deal with the identification of an autoregressive model for an observed time series and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the…

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Bayesian inference for the gravity model

引力模型的贝叶斯推断

Abstract This paper seeks to empirically extend the gravity model , which has been widely used to analyze volumes of trade between pairs of countries. We generalize the basic threshold tobit model by allowing for the inclusion of country‐specific effects into the analysis and also show how one can explore the relationship between trade volumes and a given covariate via a non‐parametric approach. We use our derived methodology to investigate the impact of a particular aspect…

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Bargaining, Reputation, and Equilibrium Selection in Repeated Games with Contracts

含合约重复博弈中的议价、声誉与均衡选择

Consider a two-person intertemporal bargaining problem in which players choose actions and offers each period, and collect payoffs (as a function of that period's actions) while bargaining proceeds. This can alternatively be viewed as an infinitely repeated game wherein players can offer one another enforceable contracts that govern play for the rest of the game. Theory is silent with regard to how the surplus is likely to be split, because a folk theorem applies. Perturbing…

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Decision Theory Applied to an Instrumental Variables Model

决策理论在工具变量模型中的应用

This paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced-form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear…

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Inference and Model Choice for Sequentially Ordered Hidden Markov Models

按出现顺序标记的隐马尔可夫模型:推断与模型选择

Summary The system equation of a hidden Markov model is rewritten to label the components by order of appearance, and to make explicit the random behaviour of the number of components, mt. We argue that this reformulation is often a good way to achieve identifiability, as it facilitates the interpretation of the posterior density, and the estimation of the number of components that have appeared in a given sample. We develop a sequential Monte Carlo algorithm for estimating…

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A Mixture Model for Multivariate Extremes

多元极值的混合模型

Summary The spectral density function plays a key role in fitting the tail of multivariate extre-mal data and so in estimating probabilities of rare events. This function satisfies moment con-straints but unlike the univariate extreme value distributions has no simple parametric form. Parameterized subfamilies of spectral densities have been suggested for use in applications, and non-parametric estimation procedures have been proposed, but semiparametric models for…

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Bayesian Density Regression

贝叶斯密度回归

Summary The paper considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors. The conditional response distribution is expressed as a non-parametric mixture of regression models, with the mixture distribution changing with predictors. A class of weighted mixture of Dirichlet process priors is proposed for the uncountable collection of mixture distributions. It is shown that this specification…

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On rates of convergence for posterior distributions in infinite-dimensional models

无限维模型中后验分布的收敛速度

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of convergence for models including the mixture of Dirichlet process model and the random Bernstein polynomial model.

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On the number of support points of maximin and Bayesian optimal designs

最大最小与贝叶斯最优设计的支撑点数目

We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior for these parameters is available. On interval parameter spaces, it was observed empirically by many authors that an increase of uncertainty in the prior information (i.e., a larger range for the parameter space in the maximin…

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Posterior convergence rates of Dirichlet mixtures at smooth densities

光滑密度下 Dirichlet 混合模型的后验收敛率

We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth is given a sequence of priors which is obtained by scaling a single prior by an appropriate order. In order to handle this problem, we derive a new general rate theorem by considering a countable covering of the parameter space whose…

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On the design-consistency property of hierarchical Bayes estimators in finite population sampling

有限总体抽样中层级贝叶斯估计量的设计一致性

We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of…

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Fast learning rates for plug-in classifiers

插入式分类器的快速学习率

It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n−1/2. The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n−1, and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are…

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Intrinsic Bayesian Estimation of Vector Autoregression Impulse Responses

向量自回归脉冲响应的内在贝叶斯估计

We propose an information-theoretic alternative to the conventional Bayesian posterior mean estimator of impulse responses in vector autoregression (VAR) models. The proposed estimator is based on the intrinsic entropy loss function, which is invariant to nonlinear transformations of parameters. Consequently, intrinsic estimation of impulse responses is equivalent to that of VAR parameters. The Bayesian estimator under the entropy loss involves a frequentist expectation of…

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Comparing Density Forecasts via Weighted Likelihood Ratio Tests

用加权似然比检验比较密度预测

We propose a test for comparing the out-of-sample accuracy of competing density forecasts of a variable. The test is valid under general conditions: The data can be heterogeneous and the forecasts can be based on (nested or nonnested) parametric models or produced by semiparametric, nonparametric, or Bayesian estimation techniques. The evaluation is based on scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. We…

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