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991.
Consider the general linear model Y = Xβ + ? , where E[??'] = σ2I and rank of X is less than or equal to the number of columns of X. It is well known that the linear parametric function λ'β is estimable if and only if λ' is in the row space of X. This paper characterizes all orthogonal matrices P such that the row space of XP is equal to the row space of X, i.e. the estimability of λ'β is invariant under P. An additional property of these matrices is the invariance of the spectrum of the information matrix X'X. An application of the results is also given. 相似文献
992.
We consider a number of estimators of regression coefficients, all of generalized ridge, or 'shrinkage' type. Results of a simulation study indicate that with respect to two commonly used mean square error criteria, two ordinary ridge estimators, one proposed by Hoerl, Kennard and Baldwin, and the other introduced here, perform substantially better than both least squares and the other estimators discussed here 相似文献
993.
Tachen Liang 《统计学通讯:理论与方法》2013,42(3):565-577
We investigate an empirical Bayes testing problem in a positive exponential family having pdf f{x/θ)=c(θ)u(x) exp(?x/θ), x>0, θ>0. It is assumed that θ is in some known compact interval [C1, C2]. The value C1 is used in the construction of the proposed empirical Bayes test δ* n. The asymptotic optimality and rate of convergence of its associated Bayes risk is studied. It is shown that under the assumption that θ is in [C1, C2] δ* n is asymptotically optimal at a rate of convergence of order O(n?1/n n). Also, δ* n is robust in the sense that δ* n still possesses the asymptotic optimality even the assumption that "C1≦θ≦C2 may not hold. 相似文献
994.
In this article, we give the asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given. 相似文献
995.
996.
The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985). This representation, together with Rychlik's (1993) results, can be used to obtain sharp bounds on the distribution (or the reliability) function and on the expected lifetime of the system. Also, this representation can be used to determine the asymptotic behavior of the hazard rate of the system when the order statistics are ordered in the hazard rate order. Moreover, the lifetime distributions of coherent systems (and in particular, of order statistics) can also be represented as generalized mixtures (that is, mixtures with some negative weights) of distributions of series system lifetimes by using the concept of the minimal signature defined by Navarro et al. (2007a). This representation can also be used to determine the final behavior of the hazard rate of the system through the behavior of the hazard rate of the series systems. In particular, it can be used to show that the order statistics are, under some conditions, asymptotically hazard rate ordered. However, in general, this result is not true, that is, the order statistics need not be hazard rate ordered. 相似文献
997.
Víctor H. Lachos Heleno Bolfarine Reinaldo B. Arellano-Valle Lourdes C. Montenegro 《统计学通讯:理论与方法》2013,42(9):1769-1786
In this article, we present EM algorithms for performing maximum likelihood estimation for three multivariate skew-normal regression models of considerable practical interest. We also consider the restricted estimation of the parameters of certain important special cases of two models. The methodology developed is applied in the analysis of longitudinal data on dental plaque and cholesterol levels. 相似文献
998.
The problem of making statistical inference about θ =P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators. 相似文献
999.
Analytical properties of regression and the variance–covariance matrix of asymmetric generalized scale mixture of multivariate Gaussian variables are presented. The analysis includes an in-depth analytical investigation of the first two conditional moments of the mixing variable. Exact computable expressions for the prediction and the conditional variance are presented for the generalized hyperbolic distribution using the inversion theorem for Fourier transforms. An application to financial log returns is demonstrated via the classical Euler approximation. The methodology is illustrated by analyzing the regression of intraday log returns for CISCO against the corresponding data from S&P 500. 相似文献
1000.
Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis. 相似文献