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1.
Abstract

In this article we study the relationship between principal component analysis and a multivariate dependency measure. It is shown, via simulated examples and real data, that the information provided by principal components is compatible with that obtained via the dependency measure δ. Furthermore, we show that in some instances in which principal component analysis fails to give reasonable results due to nonlinearity among the random variables, the dependency statistic δ still provides good results. Finally, we give some ideas about using the statistic δ in order to reduce the dimensionality of a given data set.  相似文献   

2.
Razzaghi (1987) conjectured that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency. This conjecture was proved correct by Kabe and Gupta for a wrong choice of constant covariance matrix. The present paper demonstrates that this loss of efficiency persists even with an estimated covariance matrix, thereby resulting in inefficient estimation, prediction, and confidence intervals.  相似文献   

3.
This paper deals with the problem of multicollinearity in a multiple linear regression model with linear equality restrictions. The restricted two parameter estimator which was proposed in case of multicollinearity satisfies the restrictions. The performance of the restricted two parameter estimator over the restricted least squares (RLS) estimator and the ordinary least squares (OLS) estimator is examined under the mean square error (MSE) matrix criterion when the restrictions are correct and not correct. The necessary and sufficient conditions for the restricted ridge regression, restricted Liu and restricted shrunken estimators, which are the special cases of the restricted two parameter estimator, to have a smaller MSE matrix than the RLS and the OLS estimators are derived when the restrictions hold true and do not hold true. Theoretical results are illustrated with numerical examples based on Webster, Gunst and Mason data and Gorman and Toman data. We conduct a final demonstration of the performance of the estimators by running a Monte Carlo simulation which shows that when the variance of the error term and the correlation between the explanatory variables are large, the restricted two parameter estimator performs better than the RLS estimator and the OLS estimator under the configurations examined.  相似文献   

4.
We propose a thresholding generalized method of moments (GMM) estimator for misspecified time series moment condition models. This estimator has the following oracle property: its asymptotic behavior is the same as of any efficient GMM estimator obtained under the a priori information that the true model were known. We propose data adaptive selection methods for thresholding parameter using multiple testing procedures. We determine the limiting null distributions of classical parameter tests and show the consistency of the corresponding block-bootstrap tests used in conjunction with thresholding GMM inference. We present the results of a simulation study for a misspecified instrumental variable regression model and for a vector autoregressive model with measurement error. We illustrate an application of the proposed methodology to data analysis of a real-world dataset.  相似文献   

5.
Consider an inhomogeneous Poisson process X on [0, T] whose unk-nown intensity function “switches” from a lower function g* to an upper function h* at some unknown point ?* that has to be identified. We consider two known continuous functions g and h such that g*(t) ? g(t) < h(t) ? h*(t) for 0 ? t ? T. We describe the behavior of the generalized likelihood ratio and Wald’s tests constructed on the basis of a misspecified model in the asymptotics of large samples. The power functions are studied under local alternatives and compared numerically with help of simulations. We also show the following robustness result: the Type I error rate is preserved even though a misspecified model is used to construct tests.  相似文献   

6.
In this article, we consider the estimation of a partially linear model when stochastic linear restrictions on the parameter components are assumed to hold. Based on the weighted mixed estimator, profile least-squares method, and ridge method, a weighted stochastic restricted ridge estimator of the parametric component is introduced. The properties of the new estimator are also discussed. Finally, a simulation study is given to show the performance of the new estimator.  相似文献   

7.
In this paper, the restricted almost unbiased ridge regression estimator and restricted almost unbiased Liu estimator are introduced for the vector of parameters in a multiple linear regression model with linear restrictions. The bias, variance matrices and mean square error (MSE) of the proposed estimators are derived and compared. It is shown that the proposed estimators will have smaller quadratic bias but larger variance than the corresponding competitors in literatures. However, they will respectively outperform the latter according to the MSE criterion under certain conditions. Finally, a simulation study and a numerical example are given to illustrate some of the theoretical results.  相似文献   

8.
We consider the general univariate linear model E(y) = Xb, V(y) = o2 W, W symmetric nonnegative definite. A numerically stable method based on orthogonal rotations is given for computing the least squares estimate [bcirc] of b , as well as a representation of [/(b). It is shown how to extend the computations to update these results quickly and accurately when columns or rows of (y,X) are added or taken away. One of these techniques will handle the usual F-test for the general linear hypothesis, and the updating techniques can easily handle less than full rank X and W , while checking for consistency of the model. The first section describes some disadvantages of the original formulation of the problem and gives a general formulation which avoids these. The second section describes a numerically stable method for solution, while the third considers the statistical meaning of the computed quantities. Section 4 introduces the updating techniques as continuations of the original decomposition and Section 5 treats the special case of equality constraints  相似文献   

9.
The admissibility results of Hoffmann (1977), proved in the context of a nonsingular covariance matrix are extended to the situation where the covariance matrix is singular. Admissible linear estimators in the Gauss-Markoff model are characterised and admissibility of the Best Linear Unbiased Estimator is investigated.  相似文献   

10.
Andrade and Helms (1984) study problems involving estimation and testing of linearly patterned mean and covariance matrices. They parameterize their models under the null hypothesis by using linear constraints on the alternative hypothesis parameterization. In this paper, we show that the nested models that Andrade and Helms consider can be transformed into the nested models considered by Anderson (1969, 1970, 1973) and Szatrowski (1979, 1980, 1981, 1983, 1985).  相似文献   

11.
12.
Olaf Bunke 《Statistics》2013,47(6):467-481
Bayes estimates are derived in multivariate linear models with unknown distribution. The prior distribution is defined using a Dirichlet prior for the unknown error distribution and a normal-Wishart distribution for the parameters. The posterior distribution is determined and explicit expressions are given in the special cases of location-scale and two-sample models. The calculation of self-informative limits of Bayes estimates yields standard estimates.  相似文献   

13.
A simple method of setting linear hypotheses testable by F-tests in a general linear model when the covariance matrix has a general form and is completely unknown, is provided. With some additional conditions imposed on the covariance matrix, there exist the UMP invariant tests of certain linear hypotheses. We derive them to compare the powers with those of F-tests obtained under no restrictions on the covariance matrix. The results are illustrated in a multiple regression model with some examples.  相似文献   

14.
15.
In this paper, a robust estimator is proposed for partially linear regression models. We first estimate the nonparametric component using the penalized regression spline, then we construct an estimator of parametric component by using robust S-estimator. We propose an iterative algorithm to solve the proposed optimization problem, and introduce a robust generalized cross-validation to select the penalized parameter. Simulation studies and a real data analysis illustrate that the our proposed method is robust against outliers in the dataset or errors with heavy tails.  相似文献   

16.
In this article, a generalized restricted difference-based ridge estimator is defined for the vector parameter in a partial linear model when the errors are dependent. It is suspected that some additional linear constraints may hold on to the whole parameter space. The estimator is a generalization of the well-known restricted least-squares estimator and is confined to the (affine) subspace which is generated by the restrictions. The risk functions of the proposed estimators are derived under balanced loss function. Finally, the performance of the new estimators is evaluated by a simulated data set.  相似文献   

17.
The minimum-dispersion linear unbiased estimator of a set of estimable functions in a general Gauss-Markov model with double linear restrictions is considered. The attention is focused on developing a recursive formula in which an initial estimator, obtained from the unrestricted model, is corrected with respect to the restrictions successively incorporated into the model. The established formula generalizes known results developed for the simple Gauss-Markov model.  相似文献   

18.
Consider the linear regression model, yi = xiβ0 + ei, i = l,…,n, and an M-estimate β of βo obtained by minimizing Σρ(yi — xiβ), where ρ is a convex function. Let Sn = ΣXiXiXi and rn = Sn½ (β — β0) — Sn 2 Σxih(ei), where, with a suitable choice of h(.), the expression Σ xix(e,) provides a linear representation of β. Bahadur (1966) obtained the order of rn as n→ ∞ when βo is a one-dimensional location parameter representing the median, and Babu (1989) proved a similar result for the general regression parameter estimated by the LAD (least absolute deviations) method. We obtain the stochastic order of rn as n → ∞ for a general M-estimate as defined above, which agrees with the results of Bahadur and Babu in the special cases considered by them.  相似文献   

19.
This paper is concerned with selection of explanatory variables in generalized linear models (GLM). The class of GLM's is quite large and contains e.g. the ordinary linear regression, the binary logistic regression, the probit model and Poisson regression with linear or log-linear parameter structure. We show that, through an approximation of the log likelihood and a certain data transformation, the variable selection problem in a GLM can be converted into variable selection in an ordinary (unweighted) linear regression model. As a consequence no specific computer software for variable selection in GLM's is needed. Instead, some suitable variable selection program for linear regression can be used. We also present a simulation study which shows that the log likelihood approximation is very good in many practical situations. Finally, we mention briefly possible extensions to regression models outside the class of GLM's.  相似文献   

20.
As a useful extension of partially linear models and varying coefficient models, the partially linear varying coefficient model is useful in statistical modelling. This paper considers statistical inference for the semiparametric model when the covariates in the linear part are measured with additive error and some additional linear restrictions on the parametric component are available. We propose a restricted modified profile least-squares estimator for the parametric component, and prove the asymptotic normality of the proposed estimator. To test hypotheses on the parametric component, we propose a test statistic based on the difference between the corrected residual sums of squares under the null and alterative hypotheses, and show that its limiting distribution is a weighted sum of independent chi-square distributions. We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Some simulation studies are conducted to illustrate our approaches.  相似文献   

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