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快速迭代自助法AI 解读

The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures,…

自助法迭代的离散模型AI 解读

The bootstrap can be validated by considering the sequence of P values obtained by bootstrap iteration, rather than asymptotically. If this sequence converges to a random variable with the uniform U(0,1) distribution, the bootstrap is valid. Here, the model is made discrete and finite, characterised by a three-dimensional array of probabilities. This renders bootstrap iteration to any desired order feasible. A unit-root test for a process driven by a stationary MA(1) process…

厚尾分布的参数 bootstrapAI 解读

It is known that Efron’s bootstrap of the mean of a distribution in the domain of attraction of the stable laws with infinite variance is not consistent, in the sense that the limiting distribution of the bootstrap mean is not the same as the limiting distribution of the mean from the real sample. Moreover, the limiting bootstrap distribution is random and unknown. The conventional remedy for this problem, at least asymptotically, is either the m out of n bootstrap or…

The most widely used measure of segregation is the so‐called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce…

拟合优度：一种公理化方法AI 解读

An axiomatic approach is used to develop a one-parameter family of measures of divergence between distributions. These measures can be used to perform goodness-of-fit tests with good statistical properties. Asymptotic theory shows that the test statistics have well-defined limiting distributions which are, however, analytically intractable. A parametric bootstrap procedure is proposed for implementation of the tests. The procedure is shown to work very well in a set of…

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous‐equations model. One way to obtain a confidence set for this coefficient is to invert the Anderson–Rubin (AR) test. The AR confidence sets that result have correct coverage under classical assumptions. However, AR confidence sets also have many undesirable properties. It is well known that they can be unbounded when the instruments are weak, as is true of…

Income distributions are usually characterized by a heavy right‐hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distributions admitted by econometric models. It is therefore important to determine the…

厚尾情形下的统计推断AI 解读

Income distributions are usually characterized by a heavy right‐hand tail. Apart from any ethical considerations raised by the presence among us of the very rich, statistical inference is complicated by the need to consider distributions of which the moments may not exist. In extreme cases, no valid inference about expectations is possible until restrictions are imposed on the class of distributions admitted by econometric models. It is therefore important to determine the…

工具变量回归的野生自助法检验AI 解读

We propose a wild bootstrap procedure for linear regression models estimated by instrumental variables. Like other bootstrap procedures that we proposed elsewhere, it uses efficient estimates of the reduced-form equation(s). Unlike the earlier procedures, it takes account of possible heteroscedasticity of unknown form. We apply this procedure to t tests, including heteroscedasticity-robust t tests, and to the Anderson–Rubin test. We provide simulation evidence that it works…

基尼系数的可靠推断AI 解读

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference…

工具变量线性方程中的 Bootstrap 推断AI 解读

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics--Student's t, Anderson--Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)--as functions of six random quantities leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new…

野生自助法：拒绝概率误差的改进AI 解读

The wild bootstrap is studied in the context of regression models with heteroskedastic disturbances. We show that, in one very specific case, perfect bootstrap inference is possible, and a substantial reduction in the error in the rejection probability of a bootstrap test is available much more generally. However, the version of the wild bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild…

IV 与 JIVE 估计量的矩AI 解读

We develop a method based on the use of polar coordinates to investigate the existence of moments for instrumental variables and related estimators in the linear regression model. For generalized IV estimators, we obtain familiar results. For JIVE, we obtain the new result that this estimator has no moments at all. Simulation results illustrate the consequences of its lack of moments. Copyright Royal Economic Society 2007

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就《反对使用 JIVE 的论证》答复 Ackerberg、Devereux、Blomquist 与 DahlbergAI 解读

The JAE Data Archive directory is available at http://qed.econ.queensu.ca/jae/datasets/ . Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

反对使用 JIVE 的论证AI 解读

Abstract We perform an extensive series of Monte Carlo experiments to compare the performance of two variants of the ‘jackknife instrumental variables estimator’, or JIVE, with that of the more familiar 2SLS and LIML estimators. We find no evidence to suggest that JIVE should ever be used. It is always more dispersed than 2SLS, often very much so, and it is almost always inferior to LIML in all respects. Interestingly, JIVE seems to perform particularly badly when the…

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随机占优及贫困与不平等测度的统计推断AI 解读

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and…

Bootstrap 检验的检验水平失真AI 解读

We provide a theoretical framework in which to study the accuracy of bootstrap P values, which may be based on a parametric or nonparametric bootstrap. In the parametric case, the accuracy of a bootstrap test will depend on the shape of what we call the critical value function. We show that, in many circumstances, the error in rejection probability of a bootstrap test will be one whole order of magnitude smaller than that of the corresponding asymptotic test. We also propose…

税收与转移支付归宿测度的统计推断AI 解读

We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which to assess the progressivity of taxes and benefits, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these findings characterise the sampling distribution of a number of popular indices of progressivity,…

计量经济学中的估计与推断AI 解读

Davidson and MacKinnon have written an outstanding textbook for graduates in econometrics, covering both basic and advanced topics and using geometrical proofs throughout for clarity of exposition. The book offers a unified theoretical perspective, and emphasizes the practical applications of modern theory.

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信息矩阵检验的一种新形式AI 解读

A new form of the information matrix test is developed for a wide variety of statistical models. The test is constructed against an explicit alternative with random parameter variation. It is computed using a double-length artificial regression instead of the more conventional outer-product-of-the-gradient regression, which is known to have very poor finite-sample properties. In Monte Carlo experiments for the case of univariate linear regression models, the new form…