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91.
Optimal block designs for a certain type of triallel cross experiments are investigated. Nested balanced block designs are introduced and it is shown how these designs give rise to optimal designs for triallel crosses. Several .series of nested balanced block designs, leading to optimal designs for triallel crosses are reported. 相似文献
92.
The problem of simultaneous estimation of variance components is considered for a balanced hierarchical mixed model under a sum of squared error loss. A new class of estimators is suggested which dominate the usual sensible estimators. These estimators shrink towards the geometric mean of the component mean squares that appear in the ANOVA table. Numerical results are tabled to exhibit the improvement in risk under a simple model. 相似文献
93.
Srinjoy Das 《The American statistician》2020,74(3):233-242
AbstractNonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior and boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems ensue if local linear methods are to be used. In particular, the distribution function estimator is not guaranteed to be monotone increasing, and the quantile curves can “cross.” In the article at hand, a simple method of correcting the local linear distribution estimator for monotonicity is proposed, and its good performance is demonstrated via simulations and real data examples. Supplementary materials for this article are available online. 相似文献
94.
AbstractModel misspecification in generalized linear models (GLMs) occurs usually when the linear predictor and/or the link function assumed are incorrect. This article discusses the effect of such misspecification on design selection for multinomial GLMs and proposes the use of quantile dispersion graphs to select robust designs. Due to misspecification in the model, parameter estimates are usually biased and the designs are compared on the basis of their mean squared error of prediction. Several numerical examples including a real data set are presented to illustrate the proposed methodology. 相似文献
95.
The impact of errors in the factor levels is examined on the estimation of parameters in second-order response models. Errors can occur in setting the factor levels for response surface and robust parameter design models. These errors can lead to heterogeneity of variances in model errors that make ordinary least squares estimation inappropriate. Weighted least squares and maximum likelihood estimation approaches are developed as viable alternatives where it is assumed the variances and covariances of the errors are known. Performance of these estimation techniques are examined in simulation studies for two examples. Another example is given that applies these results. 相似文献
96.
In this article, we find designs insensitive to the presence of an outlier in a diallel cross design setup for estimating a complete set of orthonormal contrasts among the effects of the general combining abilities of a set of parental lines. The criterion of robustness, suggested by Mandal (1989) in block design setup and used by Biswas (2012) in treatment-control setup, is adapted here. Complete diallel cross designs, suggested by Gupta and Kageyama (1994), and partial diallel cross designs, suggested by Gupta et al. (1995) and Mukerjee (1997), are found to be robust under certain conditions. 相似文献
97.
Generally it is very difficult to construct robust slope-rotatable designs along axial directions. Present paper focuses on modified second-order slope-rotatable designs (SOSRDs) with correlated errors. Modified robust second-order slope-rotatability conditions are derived for a general variance–covariance structure of errors. These conditions get simplified for intraclass correlation structure. A few robust second-order slope-rotatable designs (over all directions, or with equal maximum directional variance slope, or D-optimal slope) are examined with respect to modified robust slope-rotatability. It is observed that robust second-order slope-rotatable designs over all directions, or with equal maximum directional variance slope, or D-optimal slope are not generally modified robust second-order slope-rotatable designs. 相似文献
98.
Optimal symmetrical fractional factorial designs with n runs and m factors of s levels each are constructed. We consider only designs such that no two factors are aliases. The minimum moment aberration criterion proposed by Xu (2003) is used to judge the optimality of the designs. The minimum moment aberration criterion is equivalent to the popular generalized minimum aberration criterion proposed by Xu and Wu (2001), but the minimum moment criterion is simpler to formulate and employ computationally. Some optimal designs are constructed by using generalized Hadamard matrices. 相似文献
99.
Aritra Banik Bhaswar B. Bhattacharya Sandip Das 《Journal of Combinatorial Optimization》2013,26(4):655-669
The one-round discrete Voronoi game, with respect to a n-point user set $\mathcal {U}$ , consists of two players Player 1 (P1) and Player 2 (P2). At first, P1 chooses a set $\mathcal{F}_{1}$ of m facilities following which P2 chooses another set $\mathcal{F}_{2}$ of m facilities, disjoint from $\mathcal{F}_{1}$ , where m(=O(1)) is a positive constant. The payoff of P2 is defined as the cardinality of the set of points in $\mathcal{U}$ which are closer to a facility in $\mathcal{F}_{2}$ than to every facility in $\mathcal{F}_{1}$ , and the payoff of P1 is the difference between the number of users in $\mathcal{U}$ and the payoff of P2. The objective of both the players in the game is to maximize their respective payoffs. In this paper, we address the case where the points in $\mathcal{U}$ are located along a line. We show that if the sorted order of the points in $\mathcal{U}$ along the line is known, then the optimal strategy of P2, given any placement of facilities by P1, can be computed in O(n) time. We then prove that for m≥2 the optimal strategy of P1 in the one-round discrete Voronoi game, with the users on a line, can be computed in $O(n^{m-\lambda_{m}})$ time, where 0<λ m <1, is a constant depending only on m. 相似文献
100.