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建立置信集与检验渐近尺寸的通用结果
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic is a discontinuous function of a parameter.
矩条件模型中 Kleibergen LM 与条件 LR 检验的渐近尺寸
An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so. This paper shows…
L²完备与有界完备分布的实例
Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L2-completeness condition that lies between completeness and bounded completeness. We construct broad…
基于大量条件矩不等式的统计推断
We construct confidence sets for models defined by many conditional moment inequalities/equalities. The number of conditional moment restrictions can be up to infinitely many. To deal with the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify this condition in five examples from the recent partial identification literature.
可能识别失效下的 GMM 估计与一致有效的子向量推断
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CSs are…
基于条件矩不等式的非参数推断
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given…
局部识别失效下的最大似然估计与一致推断
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CSs) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter θ. This includes log likelihood, quasi-log likelihood, and least squares criterion functions.
条件异方差 AR(1) 模型中 LS、GLS 与可行 GLS 统计量的渐近理论
We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the…
子抽样、混合子抽样与尺寸校正方法的应用
This paper analyzes the properties of subsampling, hybrid subsampling, and size-correction methods in two non-regular models. The latter two procedures are introduced in Andrews and Guggenberger (2009a). The models are non-regular in the sense that the test statistics of interest exhibit a discontinuity in their limit distribution as a function of a parameter in the model. The first model is a linear instrumental variables (IV) model with possibly weak IVs estimated using…
渐近尺寸：子抽样与 m out of n Bootstrap 的问题
This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and m out of n bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is greater than the nominal level of the tests. This is due to a lack of uniformity in the pointwise asymptotics. We determine precisely the asymptotic size of such tests under a general set…
一致模型选择后估计量的子抽样推断为何出现渐近大小错误
Subsampling and the m out of n bootstrap have been suggested in the literature as methods for carrying out inference based on post-model selection estimators and shrinkage estimators. In this paper we consider a subsampling confidence interval (CI) that is based on an estimator that can be viewed either as a post-model selection estimator that employs a consistent model selection procedure or as a super-efficient estimator. We show that the subsampling CI (of nominal level…
矩不等式参数的子抽样与代入式渐近推断有效性
This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and “plug-in asymptotic” tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the pointwise asymptotic distributions of the…
弱工具变量回归中的有效双侧非相似不变检验
As Nelson and Startz [Nelson, C.R., Startz, R., 1990a. The distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one. Journal of Business 63, S125-S140; Nelson, C.R., Startz, R., 1990b. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967-976] dramatically demonstrated, standard hypothesis tests and confidence intervals in instrumental variables regression are…
弱工具变量回归中的秩检验
This paper considers tests in an instrumental variable (IVs) regression model with IVs that may be weak. Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock (2006, Econometrica 74, 715–752). In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests. Tests with such…
平稳长记忆高斯时间序列中 Whittle 最大似然估计量的有效 Edgeworth 展开
In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter . The error of the ( s − 2)-order expansion is shown to be o ( n −( s −2)/2 )—the usual independent and identically distributed rate—for a wide range of models, including the popular ARFIMA( p , d , q ) models. The expansion is valid under mild assumptions on the behavior of the…
k 步统计量与极值统计量的高阶渐近效率等价性
It is well known that a one-step scoring estimator that starts from any N 1/2 -consistent estimator has the same first-order asymptotic efficiency as the maximum likelihood estimator. This paper extends this result to k -step estimators and test statistics for k ≥ 1, higher order asymptotic efficiency, and general extremum estimators and test statistics. The paper shows that a k -step estimator has the same higher order asymptotic efficiency, to any given order, as the…
BCa 置信区间的自助法重复次数选择
This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BC a bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171–200). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specify a three-step method of choosing B that ensures that the…
受限参数空间下的假设检验
This paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis. Multivariate one-sided tests are a leading example. Optimal tests, called directed tests, are derived using a weighted average power criterion. Exact results are established first for Gaussian linear regression models with known variance. Asymptotic analogues are then established for dynamic nonlinear models. Simulation is used to compare the tests discussed in the…