A characterization of optimal vector unbiased predictor is obtained. Some properties of optimal unbiased predictors are established.
It is shown that simultaneous prediction of future random variables is equivalent to marginal prediction of these random variables.
Following Kale and Chandrasekar (1983) and Chandrasekar (1984), it is shown that the criteria proposed by ishii (1969) based
on matrices and the one proposed by Bibby and Toutenburg (1977) based on quadratic loss in the class of vector unbiased predictors
are equivalent. The above approach is illustrated with some examples. 相似文献
The inverse gaussian distribution is a flexible model which has been extensively applied in the theory of generalized linear
models and accelerated life testing where early failure times predominate. More recently it has received attention in areas
such as quality control, and as an underlying model that provides an alternative to the analysis of variance. In reliability
testing and acceptance sampling data acquisition is often in the face of scarce resources and may be both costly and time-consuming.
In such settings it is desirable to reach a statistically sound decision as quickly as possible. Based on sequential probability
ratio tests (SPRT), sequential sampling plans provide one method of arriving at a timely, statistically based decision. A
sequential sampling plan for the inverse gaussian process mean when the value of the shape parameter of the density is known
is presented in this paper. 相似文献
The sequential logit model of educational transitions has long been the dominant modeling framework for the study of inequality of educational opportunity ever since the seminal works of
[Mare, 1980] and [Mare, 1981]. But conventional applications of the model are known to be biased by the ubiquitous presence of unobserved heterogeneity. Cameron and Heckman (1998) propose a logit model that allows for two or three latent classes if the selection bias is solely generated by a person-specific component of stable unobserved heterogeneity. To evaluate the latent class logit regression estimator, this study makes use of simulated data to eliminate the influences of other problems of transition modeling. The simulation is based on five independent pairs of large samples generated from standard distributional assumptions of transition modeling. The new estimator appears to be an effective way to adjust for dynamic selection bias when family background effects are transition-invariant and sample size is in the order of ten thousand or above. By contrast, the conventional sequential logit model produces results that are very different from the data generating models. This study also considers two alternative ways to improve statistical efficiency: (1) incorporate a crude indicator of stable unobserved heterogeneity; (2) pool the effect estimates across transitions, background variables, and alternative estimators to smooth out noise under the null hypothesis of transition invariance. In addition, this study examines the impact of indicator reliability and sample size on the performance of the latent class regression models and suggests practical guidelines. 相似文献
Permutation tests for symmetry are suggested using data that are subject to right censoring. Such tests are directly relevant to the assumptions that underlie the generalized Wilcoxon test since the symmetric logistic distribution for log-errors has been used to motivate Wilcoxon scores in the censored accelerated failure time model. Its principal competitor is the log-rank (LGR) test motivated by an extreme value error distribution that is positively skewed. The proposed one-sided tests for symmetry against the alternative of positive skewness are directly relevant to the choice between usage of these two tests.
The permutation tests use statistics from the weighted LGR class normally used for making two-sample comparisons. From this class, the test using LGR weights (all weights equal) showed the greatest discriminatory power in simulations that compared the possibility of logistic errors versus extreme value errors.
In the test construction, a median estimate, determined by inverting the Kaplan–Meier estimator, is used to divide the data into a “control” group to its left that is compared with a “treatment” group to its right. As an unavoidable consequence of testing symmetry, data in the control group that have been censored become uninformative in performing this two-sample test. Thus, early heavy censoring of data can reduce the effective sample size of the control group and result in diminished power for discriminating symmetry in the population distribution. 相似文献