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用于简单假设检验的贝叶斯稳健卡方检验AI 解读

In this paper, we introduce a new Bayesian chi-squared test based on an adjusted quadratic loss function for testing a simple null hypothesis. We show that the asymptotic null distribution of our suggested test is a central chi-squared distribution under some assumptions required for the Bayesian large sample theory. We refer to our test as the Bayesian robust chi-squared test, since it is robust to parametric misspecification in the alternative model. That is, the limiting…

正态分布的新刻画与正态性检验AI 解读

We study the asymptotic covariance function of the sample mean and quantile, and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles, if and only if the underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance…

分布相等性的平滑检验AI 解读

The two-sample version of the celebrated Pearson goodness-of-fit problem has been a topic of extensive research, and several tests like the Kolmogorov-Smirnov and Cramér-von Mises have been suggested. Although these tests perform fairly well as omnibus tests for comparing two probability density functions (PDFs), they may have poor power against specific departures such as in location, scale, skewness, and kurtosis. We propose a new test for the equality of two PDFs based on…

局部错设模型下的一般设定检验AI 解读

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments–based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993,…

最大熵自回归条件异方差模型AI 解读

In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student's t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high…

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ARCH与双线性模型：非线性依赖的竞争解释AI 解读

This paper consider whether the wide acceptance of ARCH models may be at the expense of other nonlinear processes, such as bilinear models. The authors first pose a joint test for ARCH and bilinearity. A nonnested test is then suggested. The tests are then applied to three series. When GARCH models are taken as the null hypothesis, the authors fail to reject it. However, when bilinearity is taken as the null, it is rejected in two cases. Also, an out-of-sample forecasting…

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计量经济学中的统计方法AI 解读

Covers both multivariate analysis and matrix algebra. This work focuses on tests of hypotheses such as the Lagrange multiplier test. It discusses asymptotic distribution theory, and characteristic functions in depth. It is suitable for beginning graduate courses in mathematical statistics and econometrics.

备择局部误设下的模型设定检验AI 解读

It is well known that most of the standard specification tests are not robust when the alternative is misspecified. Using the asymptotic distributions of standard Lagrange multiplier (LM) test under local misspecification, we suggest a robust specification test. This test essentially adjusts the mean and covariance matrix of the usual LM statistic. We show that for local misspecification the adjusted test is asymptotically equivalent to Neyman's C (α) test, and therefore,…

自相关与条件异方差的相互作用：随机系数方法AI 解读

In applied econometrics, the authors tend to tackle specification problems one at a time rather than considering them jointly. This has serious consequences for statistical inference. One example of this is considering autocorrelation and autoregressive conditional heteroscedasticity separately. In this article, the authors consider a linear regression model with random coefficient autoregressive disturbances that provides a convenient framework to analyze autocorrelation…

市场非均衡模型中的序列相关检验与其他设定分析AI 解读

The assumption of serial independence of disturbances is the starting point of most of the work done on analyzing market disequilibrium models. We derive tests for serial dependence given normality and homoscedasticity using the Lagrange multiplier (LM) test principle. Although the likelihood function under serial dependence is very complicated and involves multiple integrals of dimensions equal to the sample size, the test statistic we obtain through the LM principle is…

预测系统性风险的调整方法AI 解读

Abstract This paper looks at the currently available beta adjustment techniques and suggests a multiple root‐linear model to adjust for the regression tendency of betas. Our empirical investigate on indicates that cross‐sectional betas are not normally distributed, but their distribution tends to normal after a square‐root transformation. The evidence from the Box‐Cox regression model and the multivariate normality observed among betas after the transformation, make the…

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