The Bayesian predictive density is found for future observations of the unknown dependent variables for a multivariate linear model with a single shift in the regression matrix.A numerical example shows that it is dan...
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The Bayesian predictive density is found for future observations of the unknown dependent variables for a multivariate linear model with a single shift in the regression matrix.A numerical example shows that it is dangerous to predict future observations with an unchanging parameter model when the appropriate model should include structural change.
Spatiotemporal tau pathology progression is regarded as highly stereotyped within each type of degenerative condition. For instance, AD has a progression of tau pathology consistently beginning in the entorhinal corte...
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Spatiotemporal tau pathology progression is regarded as highly stereotyped within each type of degenerative condition. For instance, AD has a progression of tau pathology consistently beginning in the entorhinal cortex, the locus coeruleus, and other nearby noradrenergic brainstem nuclei, before spreading to the rest of the limbic system as well as the cingulate and retrosplenial cortices. Proposed explanations for the consistent spatial patterns of tau pathology progression, as well as for why certain regions are selectively vulnerable to exhibiting pathology over the course of disease generally focus on transsynaptic spread proceeding via the brain's anatomic connectivity network in a cell-independent manner or on cell-intrinsic properties that might render some cell populations or regions uniquely vulnerable. We test connectivity based explanations of spatiotemporal tau pathology progression and regional vulnerability against cell-intrinsic explanation, using regional gene expression profiles as a proxy. We find that across both exogenously seeded and non-seeded tauopathic mouse models, the connectivity network provides a better explanation than regional gene expression profiles, even when such profiles are limited to specific sets of tau risk-related genes only. Our results suggest that, regardless of the location of pathology initiation, tau pathology progression is well characterized by a model positing entirely cell-type and molecular environment independent transsynaptic spread via the mouse brain's connectivity network. These results further suggest that regional vulnerability to tau pathology is mainly governed by connectivity with regions already exhibiting pathology, rather than by cell-intrinsic factors.
Von Rosen (1989) proposed the MLE of parameters in multivariatelinear normal model MLNM(sumfromn= lto ∞AiBiCi). This paper discusses some properties of Rosen's MLE for general distributions which includs invaria...
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Von Rosen (1989) proposed the MLE of parameters in multivariatelinear normal model MLNM(sumfromn= lto ∞AiBiCi). This paper discusses some properties of Rosen's MLE for general distributions which includs invariant, equivariant, strong consistency and asymptotic normality. Furthermore, we can construct the consistent confidence region for the parameter of experctation in MLNM(sumfromn=1to∞, AiBiCi) and obtain asymptotic distribu- tion and consistent confidence region of the linear discrimination function for canonical correlation by Kahtri (1988).
Based on the multivariate spatial rank function introduced by Mottonen and Oja [(1995), 'multivariate Spatial Sign and Rank Methods', Journal of Nonparametric Statistics, 5, 201-213] and Mottonen et al. [(1997...
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Based on the multivariate spatial rank function introduced by Mottonen and Oja [(1995), 'multivariate Spatial Sign and Rank Methods', Journal of Nonparametric Statistics, 5, 201-213] and Mottonen et al. [(1997), 'On the Efficiency of multivariate Spatial Sign and Rank Tests', Annals of Statistics, 25, 542-552], an extension of the univariate Wilcoxon regression estimate to multivariate linear models is proposed and studied. For both of the cases covariates are deterministic and i.i.d. random: we show that the proposed estimate is consistent and asymptotically normal under some appropriate assumptions. We have demonstrated that the asymptotic relative efficiency of the new regression estimate is the same as that of the generalised multivariate Hodges-Lehmann location estimates proposed by Chaudhuri [(1992), 'multivariate Location Estimation Using Extension of R-estimates Through U-statistics Type Approach', Annals of Statistics, 20, 897-916] (with m=2);thus it possesses high efficiency. Simulations show that it also performs very well in the finite sample data. While the estimate is only rotation invariant, a version that is affine invariant is proposed as well.
Let y(i) similar to N(Bx(i), Sigma), i = 1, 2,..., N, and y similar to N(B theta, Sigma) be independent multivariate observations, where the x(i)'s are known vectors, B, theta and Sigma are unknown, B being a posi...
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Let y(i) similar to N(Bx(i), Sigma), i = 1, 2,..., N, and y similar to N(B theta, Sigma) be independent multivariate observations, where the x(i)'s are known vectors, B, theta and Sigma are unknown, B being a positive definite matrix. The calibration problem deals with statistical inference concerning theta and the problem that we have addressed is the construction of confidence regions. In this article, we have constructed a region for theta based on a criterion similar to that satisfied by a tolerance region. The situation where theta is possibly a nonlinear function, say h(xi), of fewer unknown parameters denoted by the vector xi, is also considered. The problem addressed in this context is the construction of a region for xi. The numerical computations required for the practical implementation of our region are explained in detail and illustrated using an example. Limited numerical results indicate that our regions satisfy the coverage probability requirements of multiple-use confidence regions.
A generalization of the missing plot technique in univariate linearmodels to the multivariate case is given in this paper. The estimate of the missing observation vector produces the correct error matrix and the corr...
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A generalization of the missing plot technique in univariate linearmodels to the multivariate case is given in this paper. The estimate of the missing observation vector produces the correct error matrix and the correct parameter estimates but the hypothesis matrix is biased. The adjustment required to the test, for achieving the desired level of significance, when the biased hypothesis matrix is used, is derived.
This paper derives an extended version of the Haff or, more appropriately, Stein-Haff identity for an elliptically contoured distribution (ECD). This identity is then used to show that the minimax estimators of the co...
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This paper derives an extended version of the Haff or, more appropriately, Stein-Haff identity for an elliptically contoured distribution (ECD). This identity is then used to show that the minimax estimators of the covariance matrix obtained under normal models remain robust under the ECD model.
In estimation of a matrix of regression coefficients in a multivariatelinear regression model. this paper shows that minimax and shrinkage estimators under a normal distribution remain robust under an elliptically co...
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In estimation of a matrix of regression coefficients in a multivariatelinear regression model. this paper shows that minimax and shrinkage estimators under a normal distribution remain robust under an elliptically contoured distribution. The robustness of the improvement is established for both invariant and noninvariant loss functions in the above model as well as in the growth curve model. (C) 2001 Academic Press.
The concept of seemingly unrelated models is used for multivariate observations when the components of the multivariate dependent variable are governed by mutually different sets of explanatory variables and the only ...
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The concept of seemingly unrelated models is used for multivariate observations when the components of the multivariate dependent variable are governed by mutually different sets of explanatory variables and the only relation between the components is given by a fixed covariance within the observational units. A multivariate weighted least squares estimator is employed which takes the within units covariance matrix into account. In an experimental setup, where the settings of the explanatory variables may be chosen freely by an experimenter, it might be thus tempting to choose the same settings for all components to end up with a multivariate regression model, in which the ordinary and the least squares estimators coincide. However, we will show that under quite natural conditions the optimal choice of the settings will be a product type design which is generated from the optimal counterparts in the univariate models of the single components. This result holds even when the univariate models may change from component to component. For practical applications the full factorial product type designs may be replaced by fractional factorials or orthogonal arrays without loss of efficiency. (C) 2015 Elsevier Inc. All rights reserved.
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