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21.
When the method of least squares is used to estimate the parameters in a general model and the generated system of normal equations is linearly dependent, the estimate of the vector of parameters which satisfies the criterion is not unique. However, there exist certain functions of the estimated vector of parameters which are invariant to the least squares solution obtained from the normal equations. We define those invariant functions to be estimable, and present a technique to determine the functions of the parameters which are estimable for the general model. The method results in solving either a linear first order partial differential equation or a system of linear first order partial differential equations corresponding, respectively, to a single or multiple dependency between columns of the Jacobian matrix of the mean of the model. The usual results concerning estimability for linear models are a special case of the general results developed. 相似文献
22.
The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables. 相似文献
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Arthur G. Holms 《统计学通讯:模拟与计算》2013,42(1):51-71
As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 24experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge 相似文献
25.
It appears to be common practice with ridge regression to obtain a decomposition of the total sum of squares, and assign degrees of freedom, according to established least squares theory. This discussion notes the obvious fallacies of such an approach, and introduces a decomposition based on orthogonality, and degrees of freedom based on expected mean squares, for non-stochastic k. 相似文献
26.
The existing process capability indices (PCI's) assume that the distribution of the process being investigated is normal. For non-normal distributions, PCI's become unreliable in that PCI's may indicate the process is capable when in fact it is not. In this paper, we propose a new index which can be applied to any distribution. The proposed indexCf:, is directly related to the probability of non-conformance of the process. For a given random sample, the estimation of Cf boils down to estimating non-parametrically the tail probabilities of an unknown distribution. The approach discussed in this paper is based on the works by Pickands (1975) and Smith (1987). We also discuss the construction of bootstrap confidence intervals of Cf: based on the so-called accelerated bias correction method (BC a:). Several simulations are carried out to demonstrate the flexibility and applicability of Cf:. Two real life data sets are analyzed using the proposed index. 相似文献
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We consider statistical inference on parameters of a distribution when only pooled data are observed. A moment-based estimating equation approach is proposed to deal with situations where likelihood functions based on pooled data are difficult to work with. We outline the method to obtain estimates and test statistics of the parameters of interest in the general setting. We demonstrate the approach on the family of distributions generated by the Box-Cox transformation model, and, in the process, construct tests for goodness of fit based on the pooled data. 相似文献
29.
Adaptive sampling without replacement of clusters 总被引:1,自引:0,他引:1
In a common form of adaptive cluster sampling, an initial sample of units is selected by random sampling without replacement and, whenever the observed value of the unit is sufficiently high, its neighboring units are added to the sample, with the process of adding neighbors repeated if any of the added units are also high valued. In this way, an initial selection of a high-valued unit results in the addition of the entire network of surrounding high-valued units and some low-valued “edge” units where sampling stops. Repeat selections can occur when more than one initially selected unit is in the same network or when an edge unit is shared by more than one added network. Adaptive sampling without replacement of networks avoids some of this repeat selection by sequentially selecting initial sample units only from the part of the population not already in any selected network. The design proposed in this paper carries this step further by selecting initial units only from the population, exclusive of any previously selected networks or edge units. 相似文献
30.
Methodological Approaches to Assessing Risk Perceptions Associated with Food-Related Hazards 总被引:1,自引:0,他引:1
The psychometric approach developed by Slovic and his co-workers has been effectively used to assess risk perceptions associated with different food-related hazards. However, further examination (using questionnaire data and partial correlation techniques) has indicated that technological hazards are highly differentiated from lifestyle hazards, in terms of both hazard control and knowledge about the hazard. Optimistic bias was also seen to vary between hazards. Further research has focused on a particular hazard, genetic engineering. Risk perceptions associated with genetic engineering are underpinned by ethical concern and questions relating to perceived need for the technology, as well as perceptions of risk or harm. However, increasing the specificity of hazard stimuli was found to alter the factor structure of underlying risk perceptions. The utility of preference mapping procedures in determining individual differences in trust in risk regulators is also discussed. 相似文献