In this paper we investigate the effects of errors in the estimation of the covariance structure of a multivariate random vector on the prediction of unobserved components of a further vector conditional on the values...
详细信息
In this paper we investigate the effects of errors in the estimation of the covariance structure of a multivariate random vector on the prediction of unobserved components of a further vector conditional on the values of the remaining observed components of the vector. We derive an exact expression for the increase in the mean square error of the usual least squares predictor due to these estimation errors which shows that the increase is substantial for small samples.
The elemental composition of coal is essential for analysing the overall process of energy conversion systems. Simultaneous information regarding the elemental composition of coal fed into a boiler is of increasing in...
详细信息
The elemental composition of coal is essential for analysing the overall process of energy conversion systems. Simultaneous information regarding the elemental composition of coal fed into a boiler is of increasing interest for plant operation. In this study, methods of estimating the elemental composition of coal using proximate analysis and a higher heating value were developed to meet requirements in boiler operation. A novel method was developed to formulate the multivariate linear model (MLM) for predicting the elemental composition of coal by solving a set of simultaneous equations with extensive correlations between coal components and an elemental composition constraint. The maximum likelihood estimation (MLE) approach for predicting carbon, hydrogen, oxygen, nitrogen, and sulphur contents was also developed based on a series of extensive correlations among coal components. The maximum likelihood estimator employs more correlations and considers the performance of prediction residuals for each correlation, offering a better prediction accuracy than the MLM, which is based on fewer correlations and neglects prediction residuals. A total of 743 data points was used to derive the MLM and MLE models, which were validated and verified by another set of data that included the same variety of coal types. The proposed methods can estimate the complete elemental composition of coal (C, H, O, N, and S) with acceptable prediction accuracy for engineering purposes. Another important finding is that average absolute error corresponding to the measured values of nitrogen is only 14.14%, although the predicted nitrogen contents did not follow the trends of the measured values.
The multivariate linear model Y = Xβ + ∊ is used to analyze data in 2 x 2 crossover designs with either univariate or multivariate response. Diagnostics are performed on estimating the effect of interest formulated a...
详细信息
In this paper, we investigate the multivariatelinear regression of fuzzy data when model parameters are constrained by a set of linear inequalities. It is motivated by the facts that the measurement results of device...
详细信息
In this paper, we investigate the multivariatelinear regression of fuzzy data when model parameters are constrained by a set of linear inequalities. It is motivated by the facts that the measurement results of device in real-life situations are always not precise numbers and that (model) structure involving linear inequalities is usually faced to in practice. With assuming fuzzy data are seen as a possibility distribution associated to a precise realization of a random variable, we first propose a restricted fuzzy expectation/conditional maximization (RFECM) algorithm for calculating restricted maximum likelihood estimates of parameters of interest from fuzz data. We then demonstrate the convergence of RFECM algorithm. Using RFECM finally establishes the so-called likelihood-based multivariate fuzzy linear regression model with crisp inputs and fuzzy outputs, constrained by linear inequalities. Some simulations are conducted to validate the performance of our proposed model.
In this paper, we propose anew estimator for a kurtosis in a multivariate nonnormal linear regression model. Usually, an estimator is constructed from an arithmetic mean of the second power of the squared sample Mahal...
详细信息
In this paper, we propose anew estimator for a kurtosis in a multivariate nonnormal linear regression model. Usually, an estimator is constructed from an arithmetic mean of the second power of the squared sample Mahalanobis distances between observations and their estimated values. The estimator gives an underestimation and has a large bias, even if the sample size is not small. We replace this squared distance with a transformed squared norm of the Studentized residual using a monotonic increasing function. Our proposed estimator is defined by an arithmetic mean of the second power of these transformed squared norms with a correction term and a tuning parameter. The correction term adjusts our estimator to an unbiased estimator under normality, and the tuning parameter controls the sizes of the squared norms of the residuals. The family of our estimators includes estimators based on ordinary least squares and predicted residuals. We verify that the bias of our new estimator is smaller than usual by constructing numerical experiments. (C) 2005 Elsevier Inc. All rights reserved.
In this article, small-area estimation with multivariate data that follow a monotonic missing sample pattern is addressed. Random effects growth curve models with covariates are formulated. A likelihood-based approach...
详细信息
In this article, small-area estimation with multivariate data that follow a monotonic missing sample pattern is addressed. Random effects growth curve models with covariates are formulated. A likelihood-based approach is proposed for estimation of the unknown parameters. Moreover, the prediction of random effects and predicted small-area means are also discussed.
For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimator...
详细信息
For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators of SXΘ are given under each of four definitions of admissibility.
In the analysis of the multivariatelinear error-invariable model,it is assumed that the covariance matrix is nonsingular. The assumption of nonsingularity limits the number of application in *** this paper,we relax t...
详细信息
In the analysis of the multivariatelinear error-invariable model,it is assumed that the covariance matrix is nonsingular. The assumption of nonsingularity limits the number of application in *** this paper,we relax the condition of nonsingularity and consider the case when the covariance matrix may be *** least squares estimators and maximum likelihood estimators are derived for the singular covariance matrix *** results can include that in Li and Tang(2006).
作者：
Forchini, GMonash Univ
Fac Business & Econ Dept Economet & Business Stat Clayton Vic 3800 Australia
Nyblom (J. multivariate Anal. 76 (2001) 294) has derived locally best invariant test for the covariance structure in a multivariate linear model. The class of invariant tests obtained by Nyblom [9] does not coincide w...
详细信息
Nyblom (J. multivariate Anal. 76 (2001) 294) has derived locally best invariant test for the covariance structure in a multivariate linear model. The class of invariant tests obtained by Nyblom [9] does not coincide with the class of similar tests for this testing set-up. This paper extends some of the results of Nyblom [9] by deriving the locally best similar tests for the covariance structure. Moreover, it develops a saddlepoint approximation to optimal weighted average power similar tests (i.e. tests which maximize a weighted average power). (c) 2004 Elsevier Inc. All rights reserved.
In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension p and the sample size n are large. The results are given for the case that the populat...
详细信息
In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension p and the sample size n are large. The results are given for the case that the population characteristic roots have multiplicities greater than unity, and their orders are O(np) or O(n). Next, similar results are given for the asymptotic distributions of the canonical correlations when one of the dimensions and the sample size are large, assuming that the order of the population canonical correlations is O(root p) or O(1).
暂无评论