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非中心 Wishart 矩阵逆的性质AI 解读

The inverse of a noncentral Wishart matrix occurs in a variety of contexts in multivariate statistical work, including instrumental variable (IV) regression, but there has been very little work on its properties. In this paper, we first provide an expression for the expectation of the inverse of a noncentral Wishart matrix, and then go on to do the same for a number of scalar-valued functions of the inverse. The main result is obtained by exploiting simple but powerful…

空间自回归参数的调整准最大似然估计AI 解读

One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter λ in a spatial autoregression. The resulting estimator for λ has better finite sample properties compared to the QMLE for λ, especially in the presence of a large…

空间自回归模型中极大似然估计量的精确与高阶性质及推断应用AI 解读

The quasi-maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data. A rigorous analysis of the first-order asymptotic properties of the estimator, under some assumptions on the evolution of the spatial design matrix, is available in Lee (2004), but very little is known about its exact or higher-order properties. In this paper we first show that the exact cumulative distribution…

群体互动网络模型中的精确似然推断AI 解读

The paper studies spatial autoregressive models with group interaction structure, focussing on estimation and inference for the spatial autoregressive parameter λ . The quasi-maximum likelihood estimator for λ usually cannot be written in closed form, but using an exact result obtained earlier by the authors for its distribution function, we are able to provide a complete analysis of the properties of the estimator, and exact inference that can be based on it, in models that…

生成函数与短递推：非中心正态向量二次型矩的应用AI 解读

Recursive relations for objects of statistical interest have long been important for computation, and they remain so even with hugely improved computing power. Such recursions are frequently derived by exploiting relations between generating functions. For example, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other (easily computed) symmetric functions (power-sum and elementary symmetric functions;…

工具变量回归中条件似然比检验的精确性质AI 解读

For a simplified structural equation/IV regression model with one right-side endogenous variable, we derive the exact conditional distribution function of Moreira's (2003) conditional likelihood ratio (CLR) test statistic. This is used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of this function are provided for practical use. The analogous functions are also obtained for the case of testing more…

工具变量回归中多个参数的条件似然比检验AI 解读

For the problem of testing the hypothesis that all m coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest…

最高阶不变多项式的高效递推计算及应用AI 解读

The top-order zonal polynomials C k ( A ), and top-order invariant polynomials C k 1 ,…, k r ( A 1 , …, A r ) in which each of the partitions of k i , i = 1, …, r , has only one part, occur frequently in multivariate distribution theory, and econometrics — see, for example, Phillips (1980, Econometrica 48, 861–878; 1984, Journal of Econometrics 26, 387–398; 1985, International Economic Review 26, 21–36; 1986, Econometrica 54, 881–896), Hillier (1985, Econometric Theory 1,…

工具变量估计量精确性质的进一步研究AI 解读

We revisit the exact properties of two-stage least squares and limited information maximum likelihood estimators in a structural equation/instrumental variables regression under Gaussian assumptions. Simple derivations based on conditioning serve both to demystify the apparently complicated formulas, and to isolate the key quantities that determine the properties of the estimators. Some recent results obtained under weak-instrument asymptotics are sharpened and clarified by…

可能未识别的结构方程中的条件推断AI 解读

The possibility that a structural equation may not be identified casts doubt on measures of estimator precision that are usually used. Using the Fieller–Creasy problem for illustration, we argue that an observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence we argue that inference in such models should be conditioned on the observed value of that statistic (or statistics).We examine in…

n 维球面上均匀分布向量的二次型密度AI 解读

There are many instances in the statistical literature in which inference is based on a normalized quadratic form in a standard normal vector, normalized by the squared length of that vector. Examples include both test statistics (the Durbin–Watson statistic) and estimators (serial correlation coefficients). Although much studied, no general closed-form expression for the density function of such a statistic is known. This paper gives general formulae for the density in each…

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