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异方差稳健检验统计量尺寸可控的充要条件AI 解读

We revisit size controllability results in Pötscher and Preinerstorfer (2025, Econometric Theory 41, 249–301) concerning heteroskedasticity robust test statistics in regression models. For the special, but important, case of testing a single restriction (e.g., a zero restriction on a single coefficient), we provide a necessary and sufficient condition for size controllability, whereas the condition in Pötscher and Preinerstorfer (2025, Econometric Theory 41, 249–301) is, in…

有效的异方差稳健检验AI 解读

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions, and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly…

评《现代高斯—马尔可夫定理》AI 解读

We show that Theorem 4 in Hansen (2022) applies to exactly the same class of estimators as does the classical Aitken theorem. We furthermore point out that Theorems 5–7 in Hansen (2022) contain extra assumptions not present in the classical Gauss–Markov or Aitken theorem, and thus the former theorems do not contain the latter ones as special cases.

基于自助法的异方差稳健检验有多可靠？AI 解读

We develop theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models. In particular, these results provide an efficient diagnostic check, which can be used to weed out tests that are unreliable for a given testing problem in the sense that they overreject substantially. This allows us to assess the reliability of a large variety of wild bootstrap-based tests in an extensive numerical study.

模型选择后预测器的有效置信区间AI 解读

We consider inference post-model-selection in linear regression. In this setting, Berk et al. [Ann. Statist. 41 (2013a) 802–837] recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain nonstandard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to confidence intervals for post-model-selection…

自相关稳健检验的尺寸控制AI 解读

Autocorrelation robust tests are notorious for suffering from size distortions and power problems. We investigate under which conditions the size of autocorrelation robust tests can be controlled by an appropriate choice of critical value.

协方差矩阵假设的不变检验功效AI 解读

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference , 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low,…

异方差与自相关稳健检验的检验水平和功效AI 解读

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well…

单整过程负幂和的数量级AI 解读

Upper and lower bounds on the order of magnitude of $\sum\nolimits_{t = 1}^n {\lefttnq#x007C; {x_t } \righttnq#x007C;^{ - \alpha } } $ , where x t is an integrated process, are obtained. Furthermore, upper bounds for the order of magnitude of the related quantity $\sum\nolimits_{t = 1}^n {v_t } \lefttnq#x007C; {x_t } \righttnq#x007C;^{ - \alpha } $ , where v t are random variables satisfying certain conditions, are also derived.

能否估计模型选择后估计量的无条件分布？AI 解读

We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model-selection criterion such as the Akaike information criterion [AIC] or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least squares or maximum likelihood), all based on the same…

稀疏估计量与 Oracle 性质：Hodges 估计量问题的重现AI 解读

We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges’ estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity whenever the loss function is…

能否估计模型选择后估计量的条件分布？AI 解读

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion such as AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based…

收缩型估计量风险与分布估计的性能限制及一般风险下界AI 解读

We consider the problem of estimating measures of precision of shrinkage-type estimators such as their risk or distribution. The notion of shrinkage-type estimators here refers to estimators such as the James–Stein estimator and Lasso-type estimators, in addition to “thresholding” estimators such as, e.g., Hodges' so-called superefficient estimator. Although the precision measures of such estimators typically can be estimated consistently, we show that they cannot be…

模型选择与推断：事实与误解AI 解读

Model selection has an important impact on subsequent inference. Ignoring the model selection step leads to invalid inference. We discuss some intricate aspects of data-driven model selection that do not seem to have been widely appreciated in the literature. We debunk some myths about model selection, in particular the myth that consistent model selection has no effect on subsequent inference asymptotically. We also discuss an “impossibility” result regarding the estimation…

非线性函数与布朗运动收敛：超越连续映射定理AI 解读

Weak convergence results for sample averages of nonlinear functions of (discrete-time) stochastic processes satisfying a functional central limit theorem (e.g., integrated processes) are given. These results substantially extend recent work by Park and Phillips (1999, Econometric Theory 15, 269–298) and de Jong (2002, working paper), in that a much wider class of functions is covered. For example, some of the results hold for the class of all locally integrable functions,…

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模型选择后估计量的有限样本分布：一致与非一致逼近AI 解读

In Pötscher (1991, Econometric Theory 7, 163–185) the asymptotic distribution of a post-model-selection estimator, both unconditional and conditional on selecting a correct model (minimal or not), has been derived. Limitations of these results are (i) that they do not provide information on the distribution of the post-model-selection estimator conditional on selecting an incorrect model and (ii) that the quality of this asymptotic approximation to the finite-sample…

单整过程方差未必趋于无穷：平稳过程部分和的相关结果AI 解读

For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.

时间序列数组族样本二阶矩的一致收敛AI 解读

We consider abstractly defined time series arrays y t(T), 1 \le t\le T, requiring only that their sample lagged second moments converge and that their end values y1+j(T) and yT-j(T) be of order less than T½ for each j \ge 0. We show that,under quite general assumptions, various types of arrays that arise naturally in time series analysis have these properties,including regression residuals from a time series regression, seasonal adjustments and infinite variance processes…

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