간헐적인 패널 시계열 자료의 개념과 구조를 소개하고, 간헐적인 패널 시계열 자료의 모형으로 간헐적인 패널 1차 자기회귀 모형을 고려하였다. 간헐적인 패널 1차 자기회귀 모형의 동질성 검정을 위하여 Wald 검정통계량을 제안하고, 그 극한분포를 제시하였다. 또한 동질성이 만족되는 경우 시점 별 평균을 이용하여 종합한 자료로 모형을 적합하였다. 이 모형의 ...동질성 검정 통계량의 극한분포가 $\chi^{2}$분포에 잘 따르는지를 알아보기 위해 모의실험을 실시하고, 실제 자료 분석으로 지역별 월별 Mumps 자료에 간헐적인 패널 1차 자기회귀 모형을 적합하여 동질성 검정을 수행한 결과 동질성을 만족하였다. 동질성이 만족된 지역별 월별 Mumps 자료를 시점 별 평균을 이용하여 종합하고 1 차 자기회귀 모형으로 적합하였다.
The concepts and structure of intermittent panel time series data are introduced. We suggest a Wald test statistic for the test of homogeneity for intermittent panel first order autoregressive model and its limit distribution is derived. We consider the fitting the model with pooling data using sample mean at the time point if homogeneity for intermittent panel AR(1) is satisfied. We performed simulations to examine the limit distribution of the homogeneity test statistic for intermittent panel AR(1). In application, we fit the intermittent panel AR(1) for panel Mumps data and investigate the test of homogeneity.
A fundamental question in response-adaptive randomization is: What allocation proportion should we target to achieve required power while resulting in fewer treatment failures? For comparing two ...treatments, such optimal allocations are well studied in the literature. However, few authors address the question for multiple treatments and the generalization of optimal allocations is necessary in practice. We are interested in finding the optimal allocation proportion, which achieves a required power of a multivariate test of homogeneity in binary response experiments while minimizing expected treatment failures at the same time. We propose such an optimal allocation for three treatments by giving an analytical solution for the optimization problem. Numerical studies show that a response-adaptive randomization procedure that targets proposed optimal allocation is superior to complete randomization. We also discuss some future research topics and additional issues on optimal adaptive designs.
Homogeneity of dispersion parameters and zero-inflation parameters is a standard assumption in zero-inflated generalized Poisson regression (ZIGPR) models. However, this assumption may be not ...appropriate in some situations. This work develops a score test for varying dispersion and/or zero-inflation parameter in the ZIGPR models, and corresponding test statistics are obtained. Two numerical examples are given to illustrate our methodology, and the properties of score test statistics are investigated through Monte Carlo simulations.
In the statistics literature, a number of procedures have been proposed for testing equality of several groups’ covariance matrices when data are complete, but this problem has not been considered ...for incomplete data in a general setting. This paper proposes statistical tests for equality of covariance matrices when data are missing. A Wald test (denoted by
T
1
), a likelihood ratio test (LRT) (denoted by
R), based on the assumption of normal populations are developed. It is well-known that for the complete data case the classic LRT and the Wald test constructed under the normality assumption perform poorly in instances when data are not from multivariate normal distributions. As expected, this is also the case for the incomplete data case and therefore has led us to construct a robust Wald test (denoted by
T
2
) that performs well for both normal and non-normal data. A re-scaled LRT (denoted by
R
*
) is also proposed. A simulation study is carried out to assess the performance of
T
1
,
T
2
,
R, and
R
*
in terms of closeness of their observed significance level to the nominal significance level as well as the power of these tests. It is found that
T
2
performs very well for both normal and non-normal data in both small and large samples. In addition to its usual applications, we have discussed the application of the proposed tests in testing whether a set of data are missing completely at random (MCAR).
In ophthalmologic or dental studies, observations are frequently taken from multiple sites (called units), such as eyes or teeth, of each subject. In this case, observations within each subject ...(called clusters) may be dependent, although those from different subjects are independent. When a categorical observation is made from each site, application of the usual Pearson chi-square tests is invalid since sites within the same subject tend to be dependent. We propose a modified χ
2
statistic for testing no treatment effect in these cases. The proposed methods do not require correct specification of the dependence structure within cluster. Simulation studies are conducted to show the finite-sample performance of the new methods. The proposed methods are applied to real-life data.
Statistics R
a
based on power divergence can be used for testing the homogeneity of a product multinomial model. All R
a
have the same chi-square limiting distribution under the null hypothesis of ...homogeneity. R
0
is the log likelihood ratio statistic and R
1
is Pearson's X
2
statistic. In this article, we consider improvement of approximation of the distribution of R
a
under the homogeneity hypothesis. The expression of the asymptotic expansion of distribution of R
a
under the homogeneity hypothesis is investigated. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, a new approximation of the distribution of R
a
is proposed. A moment-corrected type of chi-square approximation is also derived. By numerical comparison, we show that both of the approximations perform much better than that of usual chi-square approximation for the statistics R
a
when a ≤ 0, which include the log likelihood ratio statistic.
If follow-up is made for subjects which are grouped into units, such as familial or spatial units then it may be interesting to test whether the groups are homogeneous (or independent for given ...explanatory variables). The effect of the groups is modelled as random and we consider a frailty proportional hazards model which allows to adjust for explanatory variables. We derive the score test of homogeneity from the marginal partial likelihood and it turns out to be the sum of a pairwise correlation term of martingale residuals and an overdispersion term. In the particular case where the sizes of the groups are equal to one, this statistic can be used for testing overdispersion. The asymptotic variance of this statistic is derived using counting process arguments. An extension to the case of several strata is given. The resulting test is computationally simple; its use is illustrated using both stimulated and real data. In addition a decomposition of the score statistic is proposed as a sum of a pairwise correlation term and an overdispersion term. The pairwise correlation term can be used for constructing a statistic more robust to departure from the proportional hazard model, and the overdispersion term for constructing a test of fit of the proportional hazard model.
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