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Bootstrap 单位根检验AI 解读

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op(n−1/4) and Op(n−1/2), and involve…

积分阶数未知的分数系统中的协整AI 解读

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (2001, 2003) have justified…

样本末端不稳定性检验AI 解读

This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small—possibly as small as one. The well-known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations,…

含未知函数的条件矩限制模型的有效估计AI 解读

(iii) the estimator for the asymptotic covariance of the 0 estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of 0 attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function.

连续时间流动者—留驻者模型的贝叶斯推断及劳动市场转移应用AI 解读

Abstract This paper presents Bayesian inference procedures for the continuous time mover–stayer model applied to labour market transition data collected in discrete time. These methods allow us to derive the probability of embeddability of the discrete‐time modelling with the continuous‐time one. A special emphasis is put on two alternative procedures, namely the importance sampling algorithm and a new Gibbs sampling algorithm. Transition intensities, proportions of stayers…

含类别预测变量回归中的条件均值降维AI 解读

Consider the regression of a response Y on a vector of quantitative predictors $\X$ and a categorical predictor W. In this article we describe a first method for reducing the dimension of $\X$ without loss of information on the conditional mean $\mathrm{E}(Y|\X,W)$ and without requiring a prespecified parametric model. The method, which allows for, but does not require, parametric versions of the subpopulation mean functions $\mathrm{E}(Y|\X,W=w)$, includes a procedure for…

共同未知协方差下序约束多元正态均值的同质性检验AI 解读

Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in testing the homogeneity of these mean vectors under this restriction. This problem is a multivariate extension of Bartholomew's [Biometrika} 46 (1959) 36-48]. When the covariance matrices are known, this problem has been studied by Sasabuchi, Inutsuka and Kulatunga [Hiroshima Math. J. 22 (1992) 551-560], Sasabuchi, Kulatunga and Saito [Amer. J. Math. Management Sci.…

基于 zonotope 的散布矩阵估计AI 解读

We introduce a new scatter matrix functional which is a multivariate affine equivariant extension of the mean deviation $E(|x-\mbox{Med}(x)|)$. The estimate is constructed using the data vectors (centered with the multivariate Oja median) and their angular distances. The angular distance is based on Randles interdirections. The new estimate is called the zonoid covariance matrix (the ZCM), as it is the regular covariance matrix of the centers of the facets of the zonotope…

Kleinberg 随机判别的具体统计实现：第一部分，两类分类AI 解读

The method of stochastic discrimination (SD) introduced by Kleinberg is a new method in statistical pattern recognition. It works by producing many weak classifiers and then combining them to form a strong classifier. However, the strict mathematical assumptions in Kleinberg [The Annals of Statistics 24 (1996) 2319-2349] are rarely met in practice. This paper provides an applicable way to realize the SD algorithm. We recast SD in a probability-space framework and present a…

多项式样条回归的局部渐近理论AI 解读

In this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem. The polynomial spline spaces we consider include univariate splines, tensor product splines, and bivariate or multivariate splines on triangulations. We establish asymptotic normality of the estimate and study the magnitude of the bias due to spline approximation. The asymptotic normality holds uniformly over the points where the…

可能协整序列中马尔可夫趋势的贝叶斯估计AI 解读

Stylized facts show that average growth rates of U.S. per capita consumption and income differ in recession and expansion periods. Because a linear combination of such series does not have to be a constant mean process, standard cointegration analysis between the variables to examine the permanent income hypothesis may not be valid. To model the changing growth rates in both series, we introduce a multivariate Markov trend model that accounts for different growth rates in…

方差突变、结构断裂与平稳性检验AI 解读

stochastic stationarity in time series characterized by variance shifts at some (known or unknown) point in the sample. It is shown that existing stationarity tests can be severely biased in the presence of such shifts, either oversized or undersized, with associated spurious power gains or losses, depending on the values of the breakpoint parameter and on the ratio of the prebreak to postbreak variance. Under the assumption of a serially independent Gaussian error term with…

含多元 t 创新的条件异方差动态回归模型：极大似然估计与推断AI 解读

Hessian, and information matrix of conditionally heteroscedastic dynamic regression models when the conditional distribution is multivariate t. We also derive one-sided and two-sided Lagrange multiplier tests for multivariate normality versus multivariate t based on the first two moments of the squared norm of the standardized innovations evaluated at the Gaussian pseudo-maximum likelihood estimators of the conditional mean and variance parameters. Finally, we illustrate our…

Consistent standard errors for target variance approach to GARCH estimation.

非参数扩散系数估计的偏差缩减AI 解读

In this paper, we quantify the asymptotic bias of the Florens-Zmirou (1993, Journal of Applied Probability 30, 790–804) and Jiang and Knight (1997, Econometric Theory 13, 615–645) estimator for the diffusion coefficient when the step of discretization is fixed, and then we propose a bias adjustment that partially compensates for the distortion. Also, we show that our estimators have all the asymptotic properties of the Florens-Zmirou and Jiang and Knight estimator when the…

可能未识别的结构方程中的条件推断AI 解读

The possibility that a structural equation may not be identified casts doubt on measures of estimator precision that are usually used. Using the Fieller–Creasy problem for illustration, we argue that an observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence we argue that inference in such models should be conditioned on the observed value of that statistic (or statistics).We examine in…

指数随机游走的 Dickey–Fuller 检验AI 解读

A common test in econometrics is the Dickey–Fuller test, which is based on the test statistic . We investigate the behavior of the test statistic if the data yt are given by an exponential random walk exp(Zt) where Zt = Zt−1 + σεt and the εt are independent and identically distributed random variables. The test statistic DF(T) is a nonlinear transformation of the partial sums of εt process. Under certain moment conditions on the εt we show that tends to one as λ → 0. For the…

滞后阶数随样本量变化的自协方差极限理论AI 解读

In this paper we provide some weak convergence results for sample statistics of the product of a variable with its kth-order lag. We assume the variable is a stationary vector that can be represented by linear process, and the lag length k is allowed to be a function of the sample size. Employing the Beveridge–Nelson decomposition, we derive a new functional central limit theorem for this situation and establish related stochastic integral convergence results. We then…

利用渐近枢轴统计量进行有限样本工具变量推断AI 解读

We consider the K-statistic, Kleibergen's (2002, Econometrica 70, 1781–1803) adaptation of the Anderson–Rubin (AR) statistic in instrumental variables regression. Whereas Kleibergen (2002) especially analyzes the asymptotic behavior of the statistic, we focus on finite-sample properties in a Gaussian framework. The AR statistic then has an F-distribution. The finite-sample distribution of the K-statistic is, however, affected by nuisance parameters. We consider two extreme…

加速失效时间模型下的个体生存函数估计AI 解读

We use the semiparametric accelerated failure time model to predict the survival function and its related quantities for future subjects with a given set of covariates. We derive the large‐sample distribution for the subject‐specific cumulative hazard function estimate. We then propose a simple resampling technique for constructing pointwise confidence intervals and simultaneous bands for the corresponding survival function and its quantile function over a properly selected…

相关矩阵的主成分模型AI 解读

Distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices. The intent of this paper is to reduce this disparity. Methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices. The models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically.…

球面回归AI 解读

Methods are introduced for regressing points on the surface of one sphere on points on another. Complex variables and stereographic projection are used to deal with theoretical problems of directional statistics much as they have been used historically to deal with problems in non‐Euclidean geometry. The complex plane harbours the group of Möbius transformations, and stereographic projection is used as a bridge to map these Möbius transforms to regression link functions on…

Cox 部分似然的贝叶斯论证AI 解读

In this paper, we establish both naive and formal Bayesian justifications of Cox's (1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time‐dependent covariates and time‐varying regression parameters. We establish results for continuous time as well as grouped…

含扩散与离散分量的马尔可夫过程的贝叶斯推断AI 解读

Data arising in certain radio‐tracking experiments consist of both a continuous spatial component and a discrete component related to behaviour. This leads naturally to stochastic models with a state space which is a product of continuous and discrete components. We consider a class of such models in continuous time, which can be thought of as diffusions in random environments. They are related to switching diffusion or hidden Markov models, but observations are made on both…