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41.
Product moments of bivariate chi-square distribution have been derived in closed forms. Finite expressions have been derived for product moments of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution have also been discussed. Shannon entropy of the distribution is also derived. We also discuss the Bayesian estimation of a parameter of the distribution. Results match with the independent case when the variables are uncorrelated. 相似文献
42.
The procedure-wise power functions of two strategies for balanced single-factor analysis of covariance in the presence of possibly unequal regression slopes are evaluated and illustrated. The strategies differ in the action to be taken following a re-^ jection by the preliminary test for equal slopes. The first strategy simply discards the covariate and respecifies the model as the one-way ANOVA model for testing factor effects. The second leaves the unequal slopes covariance model intact, but respecifies the factor effects hypothesis to address the factor level means adjusted to the sample average of the covariate. One additional strategy, that of testing factor effects only if the preliminary slopes test does not reject, is included for comparison purposes. Computation of the power functions requires extensive use of the results obtained in Hawkins and Han (1986) concerning the bivariate distributions of certain ratios of independent noncentral chi-square random variables. 相似文献
43.
Two test-statistics analogous to Pearson's chi-square test function - given in (1.6) and (1.7) - are investigated. These statistics utilize, apart from the number of sample elements lying in the respective intervals of the partition, their positions within the intervals too. It is shown that the test-statistics are asymptotically distributed - as the sample size N tends to infinity - according to the x 2distribution with parameter r, i.e. the number of intervals chosen. The limiting distribution of the test statistics under the null-hypothesis when N tends to the infinity and r =O(N α) (0<α<1), further the consistency of the tests based on these statistics is considered. Some remarks are made concerning the efficiency of the corresponding goodness of fit tests also; the authors intend to return to a more detailed treatment of the efficiency later. 相似文献
44.
G. J. Umphrey 《统计学通讯:模拟与计算》2013,42(5):629-635
Some clarification of statistics based on McKay's x2 approximation for the distribution of the sample coefficient of variation is presented. The conclusions of Warren (1982) are shown to result from the confusion of two definitions for the sample coefficient of variation. 相似文献
45.
Anwar H. Joarder 《Statistical Papers》2009,50(3):581-592
The exact probability density function of a bivariate chi-square distribution with two correlated components is derived. Some
moments of the product and ratio of two correlated chi-square random variables have been derived. The ratio of the two correlated
chi-square variables is used to compare variability. One such application is referred to. Another application is pinpointed
in connection with the distribution of correlation coefficient based on a bivariate t distribution.
相似文献
46.
Goodness-of-fit Tests for GEE with Correlated Binary Data 总被引:3,自引:0,他引:3
WEI PAN 《Scandinavian Journal of Statistics》2002,29(1):101-110
The marginal logistic regression, in combination with GEE, is an increasingly important method in dealing with correlated binary data. As for independent binary data, when the number of possible combinations of the covariate values in a logistic regression model is much larger than the sample size, such as when the logistic model contains at least one continuous covariate, many existing chi-square goodness-of-fit tests either are not applicable or have some serious drawbacks. In this paper two residual based normal goodness-of-fit test statistics are proposed: the Pearson chi-square and an unweighted sum of residual squares. Easy-to-calculate approximations to the mean and variance of either statistic are also given. Their performance, in terms of both size and power, was satisfactory in our simulation studies. For illustration we apply them to a real data set. 相似文献
47.
A simple random sample is observed from a population with a large number‘K’ of alleles, to test for random mating. Of n couples, nijkl have female genotype ij and male genotype kl (i, j, k, l{1,…, A‘}). The large contingency table is collapsed into three counts, n0, n1 and n2 where np is the number of couples with s alleles in common (s = 0,1, 2). The counts are estimated by np?o where n0, is the estimated probability of a couple having s alleles in common under the hypothesis of random mating. The usual chi-square goodness of fit statistic X2 compares observed (ns) with expected (np?) over the three categories, s = 0,1,2. An empirical observation has suggested that X2 is close to having a chi-square distribution with two degrees of freedom (X) despite a large number of parameters implicitly estimated in e. This paper gives two theorems which show that x is indeed the approximate distribution of X2 for large n and K1“, provided that no allele type over-dominates the others. 相似文献
48.
In this article, we examine the limiting behavior of generalized method of moments (GMM) sample moment conditions and point out an important discontinuity that arises in their asymptotic distribution. We show that the part of the scaled sample moment conditions that gives rise to degeneracy in the asymptotic normal distribution is T-consistent and has a nonstandard limiting distribution. We derive the appropriate asymptotic (weighted chi-squared) distribution when this degeneracy occurs and show how to conduct asymptotically valid statistical inference. We also propose a new rank test that provides guidance on which (standard or nonstandard) asymptotic framework should be used for inference. The finite-sample properties of the proposed asymptotic approximation are demonstrated using simulated data from some popular asset pricing models. 相似文献
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