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生成并标记所有正规分数因子设计或区组的方法
SUMMARY By exploiting the vector space structure of regular qn – m-designs we construct and demonstrate a method for generating all such designs, without repetition, along with their confounded interactions, resolution numbers, alias sets and a decodable design number.
方向变量回归模型的最优设计
Optimal designs are described for three cases. In the first, the dependent variable is a scalar which regresses on a direction, using the trigonometric or spherical harmonic systems. In the next case, the predictors are scalars whilst the regressor is a direction; models for this situation were introduced by Gould (1969). In the third case both the predictors and the regressor are directions, and a vector regression is suggested.
方向变量回归模型的最优设计
Optimal designs are described for three cases. In the first, the dependent variable is a scalar which regresses on a direction, using the trigonometric or spherical harmonic systems. In the next case, the predictors are scalars whilst the regressor is a direction; models for this situation were introduced by Gould (1969). In the third case both the predictors and the regressor are directions, and a vector regression is suggested.
方向数据的判别分析
Expressions are obtained for discriminant statistics when sampling from circular and spherical normal distributions. Some moments and sampling distributions are obtained for these statistics. Also some expressions for the theoretical error probabilities are evaluated.
方向数据的判别分析
Expressions are obtained for discriminant statistics when sampling from circular and spherical normal distributions. Some moments and sampling distributions are obtained for these statistics. Also some expressions for the theoretical error probabilities are evaluated.
凸损失在回归设计问题中的应用
Summary A general linear regression function is to be observed at n points in order to estimate a known linear combination of the unknown parameters. The n points and the estimator are to be optimum in some sense and in this paper the main criterion for optimality involves uniformly minimizing certain convex loss functions. Three main sets of results are obtained, followed by some further results for normally distributed errors.
一般凸损失下回归问题的最优设计
The polynomial regression model in which the errors are independent and identically distributed, is considered, and attention is focused on the estimate of β8, the coefficient, of the term of highest degree. A design D is a set of n values in [−1, 1] of the concomitant, variable x, and the least-squares estimator of β8, when the design D is used, is donoted by β(D). Then D* is said to dominate D if, for every continuous convex function c, E[c{β(D*)})≤= E[c{β(D)}. Does there…
一般凸损失下回归问题的最优设计
The polynomial regression model in which the errors are independent and identically distributed, is considered, and attention is focused on the estimate of β8, the coefficient, of the term of highest degree. A design D is a set of n values in [−1, 1] of the concomitant, variable x, and the least-squares estimator of β8, when the design D is used, is donoted by β(D). Then D* is said to dominate D if, for every continuous convex function c, E[c{β(D*)})≤= E[c{β(D)}. Does there…