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遗漏结构不稳定时协方差估计与过度识别检验的极限行为AI 解读

We consider the limiting behavior of the overidentifying restrictions test in the presence of neglected structural instability at a single “break point.” It is shown that the test need not be consistent against this type of misspecification. If it is consistent then it emerges that the limiting behavior of this test statistic depends on the covariance matrix estimator employed. In this paper we consider the case in which a heteroskedasticity autocorrelation covariance (HAC)…

极限分布对目标参数连续并非 Bootstrap 有效性的必要条件AI 解读

It is well known that the unrestricted bootstrap estimator of the slope parameter in the random walk model without drift converges to a random distribution. This bootstrap failure is commonly attributed to the discontinuity of the limit distribution of the least-squares estimator in the parameter of interest. We demonstrate by counterexample that this type of continuity is not essential for the validity of the bootstrap nor is it essential that the rate of convergence of the…

基于广义经验似然的矩条件模型选择准则AI 解读

This paper proposes model selection criteria (MSC) for unconditional moment models using generalized empirical likelihood (GEL) statistics. The use of GEL-statistics in lieu of J-statistics (in the spirit of Andrews, 1999, Econometrica 67, 543–564; and Andrews and Lu, 2001, Journal of Econometrics 101, 123–164) leads to an alternative interpretation of the MSCs that emphasizes the common information-theoretic rationale underlying model selection procedures for both…

AR(1) 模型、单位根与调整剖面似然AI 解读

An unobserved components and a conventional first-order autoregressive (AR) model with constant are analyzed with the adjusted profile likelihood of Cox and Reid (1987, Journal of the Royal Statistical Society, Series B 49, 1–39; 1993, Journal of the Royal Statistical Society, Series B 55, 467–71). Both the unobserved components model and the Cox–Reid adjustment can provide more accurate estimates of an AR coefficient of unity. The unobserved components model yields more…

Durbin–Watson statistic and random individual Effects.

A Mixingale inequality using an exponential moment.

Consistent standard errors for target variance approach to GARCH estimation.

A concise derivation of the Wallace and Hussain fixed effects transformation.

循环神经网络的可识别性AI 解读

We examine the identifiability of a nonlinear state space system under general assumptions. The discrete time evolution of the state is generated by a recurrent Elman network. For a large set of Elman networks we determine the class of observationally equivalent minimal systems, i.e., minimal systems that exhibit the same input-output behavior.The authors are grateful for discussions with M. Deistler and D. Bauer. A.A. Al-Falou was funded by the ERNSI network within the…

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…

密度泛函及其期权定价应用AI 解读

We present a method of estimating density-related functionals, without prior knowledge of the density's functional form. The approach revolves around the specification of an explicit formula for a new class of distributions that encompasses many of the known cases in statistics, including the normal, gamma, inverse gamma, and mixtures thereof. The functionals are based on a couple of hypergeometric functions. Their parameters can be estimated, and the estimates then reveal…

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…

02.4.2 结构方程模型拟合优度检验中一个矩阵的秩：解答AI 解读

On the rank of a matrix useful in goodness-of-fit testing of structural equation models—solution.An excellent solution was independently proposed by A. Satorra and H. Neudecker, the posers of the problem.

On Hadamard product of square roots of correlation matrices—solution.

Regression with an evaporating logarithmic trend—solution.

The asymptotic distribution of the Dickey–Fuller statistic under nonnegativity constraint.

Normal's deconvolution and the independence of sample mean and variance.

问题 02.3.2：不当加权最小二乘——解答AI 解读

Badly weighted least squares—solution.An excellent solution was independently proposed by Geert Dhaene. A proof for the case p = 1 based on the convexity of Laplace transforms was also provided by Koenker and Portnoy, the posers of the problem.

齐次函数的非参数估计AI 解读

Consider the regression , where and the exact functional form of f is unknown, although we do know that f is homogeneous of known degree r. Using a local linear approach, we examine two ways of nonparametrically estimating f: (i) a “direct” approach and (ii) a “projection based” approach. We show that depending upon the nature of the conditional variance , one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to…

多期条件矩限制下最优非线性工具变量的形式AI 解读

We present the form of the optimal instrument in a system of multiperiod conditional moment restrictions in the presence of conditional heteroskedasticity. Using Hansen's (1985, Journal of Econometrics 30, 203–228) and Hansen, Heaton, and Ogaki's (1988, Journal of the American Statistical Association 83, 863–871) work on efficiency bounds for generalized method of moments estimators, we show that this form is an autoregressive recurrence parametrized by a few auxiliary…

E-Gini 指数的渐近估计AI 解读

Under minimal assumptions on the distribution of income, we demonstrate that Chakravarty's empirical (1988, International Economic Review 29, 147–156) E-Gini index is consistent and asymptotically normal. We also derive an explicit formula for the asymptotic variance of the index and then construct a consistent and computationally straightforward estimator for it.Sincere thanks are due to the co-editor Oliver B. Linton and two anonymous referees whose constructive criticism,…