The payer considers an extension of Tran Van Hoa's family of 2SHI (two Stage hierarchical information) estimators for the coefficient vector of a linear regression model and derives the conditions for the dominanc...
详细信息
The payer considers an extension of Tran Van Hoa's family of 2SHI (two Stage hierarchical information) estimators for the coefficient vector of a linear regression model and derives the conditions for the dominance of the 2SHI estimator over the OLS and Stein rule estimators under a Generalized Pitman Nearness (GPN) criterion when the disturbance variable is small.
An ultrastructural model framework of linearregression relationship between the study and explanatory variables is considered which allows a comprehensive treatment of the classical linear regression model which is f...
详细信息
An ultrastructural model framework of linearregression relationship between the study and explanatory variables is considered which allows a comprehensive treatment of the classical linear regression model which is free from contamination and the two popular forms, viz., the functional and the structural, of the measurement error model under one roof. Assuming knowledge of the variance of the measurement errors associated with explanatory variable, a consistent class of the slope parameter has been considered and large-sample asymptotic properties have been studied when distributions of measurement errors are not necessarily normal.
The M-estimators are proposed for the linear regression model with random design when the response observations are doubly censored. The proposed estimators are constructed as some functional of a Campbell-type estima...
详细信息
The M-estimators are proposed for the linear regression model with random design when the response observations are doubly censored. The proposed estimators are constructed as some functional of a Campbell-type estimator (F) over cap(n) for a bivariate distribution function based on data which are doubly censored in one coordinate. We establish strong uniform consistency and asymptotic normality of (F) over cap(n) and derive the asymptotic normality of the proposed regression M-estimators through verifying their Hadamard differentiability property. As corollaries, we show that our results on the proposed M-estimators also apply to other types of data such as uncensored observations, bivariate observations under univariate right censoring, bivariate right-censored observations, and so on. Computation of the proposed regression M-estimators is discussed and the method is applied to a doubly censored data set, which was encountered in a recent study on the age-dependent growth rate of primary breast cancer.
The change-point problem for normal regressionmodels is considered here as the problem of choosing the hypothesis H-0 of no change or one of the hypotheses H-i that one or more parameters change after the ith observa...
详细信息
The change-point problem for normal regressionmodels is considered here as the problem of choosing the hypothesis H-0 of no change or one of the hypotheses H-i that one or more parameters change after the ith observation. The observations are often associated with a known increasing sequence tau(i) (for example, tau(i) is the date of the ith observation). It then seems natural to introduce a quadratic loss function involving (tau(i) - tau(j))(2) for selecting H-j instead of the true hypothesis H-j. A Bayes optimal invariant procedure is derived within such a framework and compared to previous proposals. When H-0 is rejected, large errors may arise in the estimation of the change point. To get around this difficulty another procedure is introduced whose main feature is to select one of the H-i's when H-0 is rejected only if there is sufficient evidence in favour of this choice.
Postulating a super-population linear regression model for a variable of interest on an auxiliary variable we consider design-based estimation of regression coefficients on drawing a sample with unequal probabilities ...
详细信息
Postulating a super-population linear regression model for a variable of interest on an auxiliary variable we consider design-based estimation of regression coefficients on drawing a sample with unequal probabilities from a survey population. Asymptotic design-cum-model based variance estimation procedures are proposed.
This investigation proposes consistent nonparametric tests for the hypothesis that a distribution is symmetric about a known median, taken without loss of generality to be zero. These tests are based on the L2 norm an...
详细信息
This investigation proposes consistent nonparametric tests for the hypothesis that a distribution is symmetric about a known median, taken without loss of generality to be zero. These tests are based on the L2 norm and the celebrated kernel method of density estimation. The test statistics when appropriately centered and scaled are asymptotically normal under the null hypothesis. Generalization of the procedure to the case of testing symmetry of residuals in the linear regression model is given offering a more advantageous procedure to that of Fan and Gencay (1995). The procedure is also shown to apply to the case of testing "bivariate symmetry", cf. Hollander (1971).
Summ. & Conclusions - In the proportional hazards model the effect of a covariate is assumed to be time-invariant, In this paper a graphical method based on a linear regression model (LRM) is used to test whether ...
详细信息
Summ. & Conclusions - In the proportional hazards model the effect of a covariate is assumed to be time-invariant, In this paper a graphical method based on a linear regression model (LRM) is used to test whether this assumption is realistic. The variation in the effect of a covariate is plotted against time, The slope of this plot indicates the nature of the influence of a covariate over time, A covariate is time-dependent if a drastic change in the slope of the plot is found and the time-point, at which this drastic change occurs provides a guideline in redefining a time-dependent covariate into two or more time-independent covariates. This method is applied to failure data of cables used for supplying power to electric mine loaders. The results obtained by applying only the proportional hazards model were misleading as the graphical method based on the LRM showed that one covariate was highly time-dependent, This graphical method should be used to supplement the proportional hazards model, not as a separate method. This avoids misinterpretation of the influence of a time-dependent covariate in the proportional hazards model, The proportional hazards model should be used to identify the most important covariates, while the LRM should be used as an explanatory tool to check the consistency of the influence of the covariates. The LRM involves matrix computations which can be quite time consuming for large data-sets, Also, tests for the statistically significant effect of a covariate are not get well established in the model.
The general linear hypothesis is usually tested by means of an F-statistic dependent on the least squares estimator. In this paper, a class of linear estimators is identified which can also serve as a basis for such a...
详细信息
The general linear hypothesis is usually tested by means of an F-statistic dependent on the least squares estimator. In this paper, a class of linear estimators is identified which can also serve as a basis for such an F-statistic. Conditions are derived under which this F-statistic coincides with the usual one. This opens the possibility of constructing minimax-estimators which dominate LS with respect to risk, yielding the same test results.
We consider the problem of estimating the parameter vector in the linearmodel when observations on the independent variables are partially missing or incorrect. New estimators are developed, which systematically comb...
详细信息
We consider the problem of estimating the parameter vector in the linearmodel when observations on the independent variables are partially missing or incorrect. New estimators are developed, which systematically combine prior information with the incomplete data. We compare these methods with the alternative strategy of deleting incomplete observations.
In this paper we investigate under which conditions it is preferable to use proxies or to omit variables from the linear regression model with respect to the matrix mean square error criterion. Furthermore, some atten...
详细信息
In this paper we investigate under which conditions it is preferable to use proxies or to omit variables from the linear regression model with respect to the matrix mean square error criterion. Furthermore, some attention is paid to the admissibility of the proxies-based least squares estimator.
暂无评论