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短程与长程依赖下离散傅里叶变换渐近独立的充要条件AI 解读

Let $\{X_t\}$ be a stationary time series and let $d_T(\lambda)$ denote the discrete Fourier transform (DFT) of $\{X_0,\ldots,X_{T-1}\}$ with a data taper. The main results of this paper provide a characterization of asymptotic independence of the DFTs in terms of the distance between their arguments under both short- and long-range dependence of the process $\{X_t\}$. Further, asymptotic joint distributions of the DFTs $d_T(\lambda_{1T})$ and $d_T(\lambda_{2T})$ are also…

平稳高斯强相依过程参数最大似然估计的有效渐近展开AI 解读

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA-type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin's general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood…

无限维正态分布均值的自适应贝叶斯推断AI 解读

We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a "smoothness condition," we first derive the convergence rate of the posterior distribution for a prior that is the infinite product of certain normal distributions and compare with the minimax rate of convergence for point estimators. Although the posterior distribution can achieve the…

具有未知协变量阈值变点的 Cox 回归估计AI 解读

We consider a nonregular Cox model for independent and identically distributed right censored survival times, with a change-point according to the unknown threshold of a covariate. The maximum partial likelihood estimators of the parameters and the estimator of the baseline cumulative hazard are studied. We prove that the estimator of the change-point is n-consistent and the estimator of the regression parameters are $n^{1/2}$-consistent, and we establish the asymptotic…

低重复次数方差分量模型中的推断AI 解读

In components of variance models the data are viewed as arising through a sum of two random variables, representing between- and within-group variation, respectively. The former is generally interpreted as a group effect, and the latter as error. It is assumed that these variables are stochastically independent and that the distributions of the group effect and the error do not vary from one instance to another. If each group effect can be replicated a large number of times,…

复合决策理论与经验贝叶斯方法：特邀论文AI 解读

Introduction.Compound decision theory and empirical Bayes methodology, acclaimed as "two breakthroughs" by Neyman (1962), are the most important contributions of Herbert Robbins to statistics.The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related developments.Robbins introduced compound decision theory in 1950 at the Second Berkeley Symposium on Mathematical Statistics and…

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向量误差修正模型面板的似然协整分析AI 解读

panels of a fixed number of vector error-correction (VEC) models. We obtain likelihood ratio statistics to test for a common cointegration rank across the individual VEC models with both heterogeneous and homogeneous cointegrating vectors. Their limiting distributions are a summation of the limiting behavior of Johansen trace statistics. We extend the asymptotic distribution theory to cover the case of an infinite cross-sectional dimension. We apply the framework to a…

条件资产定价模型的有效估计AI 解读

parameters of multivariate generalized autoregressive conditional heteroscedasticity-in-mean models when the disturbances have a conditional distribution assumed to be elliptically symmetric but otherwise unrestricted. Under high-level assumptions, the resulting estimator achieves the asymptotic semiparametric efficiency bound. The elliptical symmetry assumption allows us to avert the curse of dimensionality problem that would otherwise arise in estimating the unknown error…

半参数家庭等价尺度的有效估计：来自南非的证据AI 解读

base-independent equivalence scales. The partial linear index specification permits simultaneous estimation across multiple household types and multiple goods and also the incorporation of continuous and discrete household attributes. Furthermore, asymptotic properties of estimated equivalence scales and tests of base independence are readily obtained. The efficiency gains from the proposed models and estimators are particularly helpful for developing country data where…

塔科马的气味AI 解读

A variant of the average derivative estimator is developed to construct an index measuring the effects of a copper smelter on house prices in Tacoma, Washington. The estimated average derivative index is smooth and has lower standard errors than regression coefficients estimated separately across discrete time periods. The dataset spans the time of initial rumors of Superfund site designation, the closing of the smelter, Superfund site designation, and the start of cleanup…

用于决策的回归建模与元分析AI 解读

Regression models are often used, explicitly or implicitly, for decision making. However, the choices made in setting up the models (e.g., inclusion of predictors based on statistical significance) do not map directly into decision procedures. Bayesian inference works more naturally with decision analysis but presents problems in practice when noninformative prior distributions are used with sparse data. We do not attempt to provide a general solution to this problem, but…

单位根检验的功效函数与功效包络AI 解读

This paper studies power functions and envelopes for covariate augmented unit root tests. The power functions are calculated by integrating the characteristic function, allowing accurate evaluation of the power envelope and the power functions. Using the power functions, we study the selection among point optimal invariant unit root tests. An “optimal” point optimal test is proposed based on minimizing the integrated power difference. We find that when there are covariate…

《金融计量经济学》书评：Gourieroux与Jasiak著AI 解读

Over the past decade financial econometrics has evolved from a small subfield of econometrics to a rapidly growing area of research that maintains its own journals and dominates the applied time series sessions in many major conferences. Financial econometrics is a conglomerate of statistical models and techniques to summarize regular features of financial data sets and to evaluate theoretical models and hypotheses that have been set forth by financial economists. Besides…

若干季节单位根检验的渐近性质AI 解读

This paper analyzes the large sample behavior of the seasonal unit root tests of Dickey, Hasza, and Fuller (1984, Journal of the American Statistical Association 79, 355–367) when applied to a series that admits a unit root at the zero but not seasonal spectral frequencies. We show that in such cases the Dickey et al. statistics have nondegenerate limiting distributions. Consequently, there is a nonzero probability that, taken in isolation, they will lead the applied…

方差比检验的渐近功效AI 解读

The variance-ratio (VR) test statistic, which is based on k -period differences of the data, is commonly used in empirical finance and economics to test the random walk hypothesis. We obtain the asymptotic power function of the VR test statistic when the differencing period k is increasing with the sample size n such that k / n → δ > 0. We show that the test is inconsistent against a variety of mean-reverting alternatives, confirm the result in simulations, and then…

向量 ARMA-GARCH 模型的渐近理论AI 解读

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive…

检测 GMM 中的识别不足AI 解读

This paper proposes a test of the null of underidentification in the nonlinear-in-parameters generalized method of moments model. It can be thought of as a nonlinear analog of the usual linear instrumental variables first-stage F-test. It can be used as a diagnostic to warn a researcher when conventional asymptotic theory is unlikely to work well.I am grateful to Don Andrews, Jon Faust, John Fernald, Jim Stock, and two anonymous referees for their helpful comments on earlier…

自回归过程中的多步预测AI 解读

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h > 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction model's coefficients…

异方差因子分析AI 解读

Two moment‐based model‐fitting procedures for the heteroscedastic factor analysis model are introduced and compared. The procedures produce consistent parameter estimators and asymptotically valid inferences for heteroscedasticity without specifying the distributional forms for the factor and heteroscedastic errors. Also, an individual‐specific inference procedure for the factor score is developed. Simulation studies show the practical usefulness of the procedures. An…

工作相关结构误设、参数估计与协变量设计对广义估计方程性能的影响AI 解读

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three features of the analysis,…

利用形状约束回归检验线性与凸回归函数AI 解读

An unbiased test for the appropriateness of the simple linear regression model is presented. The null hypothesis is that the underlying regression function is indeed a line, and the alternative is that it is convex. The exact distribution for a likelihood ratio test statistic is that of a mixture of beta random variables, with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction. Simulations show that…

Bürmann展开与可加性检验AI 解读

We propose a Lagrange multiplier test for additivity based on the Bürmann expansion of a conditional mean function. The asymptotic null distribution of the test is shown to be x2, under some regularity conditions. In contrast, the Lagrange multiplier test proposed by Chen et al. (1995) is based on the Volterra expansion of the conditional mean function. We discuss some desirable advantages of the Bürmann expansion over the Volterra expansion for nonlinear time series…