Journal ArticleDOI
Estimation of Heteroscedastic Variances in Linear Models
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TLDR
In this paper, a new method known as MINQUE (Minimum Norm Quadratic Unbiased Estimation) is introduced for the estimation of the heteroscedastic variances.Abstract:
Let Y=Xβ+e be a Gauss-Markoff linear model such that E(e) = 0 and D(e), the dispersion matrix of the error vector, is a diagonal matrix δ whose ith diagonal element is σi 2, the variance of the ith observation yi. Some of the σi 2 may be equal. The problem is to estimate all the different variances. In this article, a new method known as MINQUE (Minimum Norm Quadratic Unbiased Estimation) is introduced for the estimation of the heteroscedastic variances. This method satisfies some intuitive properties: (i) if S 1 is the MINQUE of Σ piσi 2 and S 2 that of Σqiσi 2 then S 1+S 2 is the MINQUE of σ(pi + qi )σi 2, (ii) it is invariant under orthogonal transformation, etc. Some sufficient conditions for the estimation of all linear functions of the σi 2 are given. The use of estimated variances in problems of inference on the β parameters is briefly indicated.read more
Citations
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Journal ArticleDOI
A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity
TL;DR: In this article, a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic is presented, which does not depend on a formal model of the structure of the heteroSkewedness.
Journal ArticleDOI
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
TL;DR: In this paper, the authors proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects, and developed a satisfactory asymptotic theory for estimators of variance components.
Journal ArticleDOI
Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis
TL;DR: In this paper, a class of weighted jackknife variance estimators for the least square estimator by deleting any fixed number of observations at a time was proposed, and three bootstrap methods were considered.
Journal ArticleDOI
Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange *
TL;DR: In this paper, a new dataset consisting of six years of real-time exchange rate quotations, macroeconomic expectations, and macroeconomic realizations (announcements) was used to characterize the conditional means of U.S. dollar spot exchange rates versus German Mark, British Pound, Japanese Yen, Swiss Franc, and Euro.
Journal ArticleDOI
Some statistical aspects of partitioning genotype-environmental components of variability.
TL;DR: An alternative approach for dividing genotype-environment interaction into components, one corresponding to each genotype, is proposed, and the optimum properties are discussed, which are then extended to take into account a covariate.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
J. Aitchison,C. Radhakrishna Rao +1 more
TL;DR: Causal inference in statistics: An overview Linear Statistical Inference And Its Bayesian inference Wikipedia Springer Series in Statistics Stanford University Statistical Modeling, Causal Inference, and Social Science.
Journal ArticleDOI
Computing the distribution of quadratic forms in normal variables
TL;DR: In this paper, exact and approximate methods for computing the distribution of quadratic forms in normal variables are given for a given value x, around the probability P{Q > x}.
Journal ArticleDOI
The Examination and Analysis of Residuals
F. J. Anscombe,John W. Tukey +1 more
TL;DR: A number of methods for examining the residuals remaining after a conventional analysis of variance or least-squares fitting have been explored during the past few years as discussed by the authors, and a variety of these techniques more easily available, so that they can be tried out more widely.
Book ChapterDOI
The Analysis of Disturbances in Regression Analysis
TL;DR: In this article, the T-element column vector of values taken by the dependent variable is used to estimate the parameter vector of the equation, where y is the T element column vector and u a column of T disturbance.