Moran-Flavored Tests with Nuisance Parameters: Examples
Moran-Flavored Tests with Nuisance Parameters: Examples
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DOI：
10.1007/978-3-662-05617-2_3
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发表时间：
2004
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影响因子：
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通讯作者：
J. Pinkse
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作者：
J. Pinkse
自从Moran （1950b）最初提出相关性检验以来，许多作者研究了它在不同条件下的性质。在本章中，我将展示如何使用Pinkse（1999）的新技术结果来验证Moran检验或其相互关联的变体（参见Box和Jenkins， 1976，详细讨论时间序列模型中的相互关联）在独立性的零假设下确实具有极限正态分布。许多空间依赖性测试都是基于Moran测试统计量，或者可以以Moran口味测试的形式编写。通常采用莫兰式测试形式的测试的一个主要例子是拉格朗日乘数（LM）或分数测试（Burridge, 1980）。l在Anselin（1988,1997）中有一个一般性的讨论和许多有用的参考文献。在空间回归模型背景下探索LM测试的其他作者有Anselin和Rey (1991)， Anselin和Florax（1995）和Anselin等人（1996）。Pinkse和Slade（1998）在probit模型中提出了一种基于模拟的测试。也可以进行非参数的空间独立性测试。如果样本量足够大，则空间独立性的非参数检验拒绝空间独立性零假设的任何替代方案。在Brett和Pinkse（1997）中可以找到非参数空间独立性检验，这是基于Pinkse（1998）对序列独立性的类似检验。关于空间依赖性测试的大量文献进一步包括Anselin and Kelejian（1997）、Kelejian and Robinson（1995）和King（1981）。Cliff和Ord（1972,1973,1981）以及Sen（1976）在相当一般的条件下研究了Moran检验的性质。Sen只研究了相关结构被观察到的变量的情况，尽管他处理了这些变量的平均值未被观察到时产生的小麻烦参数问题。Cliff和Ord（1981）也考虑了这样一种情况，即待研究的相关性变量是线性回归模型中的误差。他们正式证明了干扰参数的向量，在这种情况下是回归系数的向量，不影响极限分布。Moran检验用于检测同一变量在不同位置之间的相关性。Pinkse（1999）的检验允许对两者之间的相关性进行检验
Since Moran (1950b) originally proposed his test of correlation, many authors have investigated its properties under varying conditions. In this chapter I demonstrate how new technical results of Pinkse (1999) can be used to verify that the Moran test, or a cross-correlation variant thereof (see Box and Jenkins, 1976, for a detailed discussion of cross-correlation in time series models), indeed has a limiting normal distribution under the null hypothesis of independence. Many tests for spatial dependence are based on the Moran test statistic, or can be written in the form of a Moran-flavored test. A prime example of a test that often takes the form of a Moran-flavored test is the Lagrange Multiplier (LM) or score test (Burridge, 1980, made this observation). l A general discussion and many useful references can be found in Anselin (1988, 1997). Other authors who have explored LM tests in the context of spatial regression models are Anselin and Rey (1991), Anselin and Florax (1995c) and Anselin et al.(1996). Pinkse and Slade (1998) propose a simulation-based test in probit models. It is also possible to test for spatial independence nonparametrically. A nonparametric test of spatial independence rejects any alternative to the null hypothesis of spatial independence provided that the sample size is big enough. A nonparametric spatial independence test can be found in Brett and Pinkse (1997), which is based on a similar test for serial independence by Pinkse (1998). The vast literature on testing for spatial dependence further includes Anselin and Kelejian (1997), Kelejian and Robinson (1995), and King (1981). Cliff and Ord (1972, 1973, 1981) and Sen (1976) have studied the properties of the Moran test under fairly general conditions. Sen only studies the case where the variables whose correlation structure is being investigated are observed, although he deals with a minor nuisance parameter problem arising when the mean of these variables is unobserved. Cliff and Ord (1981) also consider the case in which the variables whose correlation is to be studied are errors in a linear regression model. They formally prove that the vector of nuisance parameters, in this case the vector of regression coefficients, does not affect the limiting distribution. The Moran test is used to detect the correlation between the same variable at different locations. Pinkse's (1999) test allows for the correlation to be tested between