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Volume 41 (2012)
- Issue 3 Pages 129-
- Issue 2 Pages 79-
- Issue 1 Pages 1-
Volume 41, Issue 1
Displaying 1-4 of 4 articles from this issue
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Contributed Papers
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Naohiro Kato, Satoshi KurikiArticle type: Contributed Papers
2012 Volume 41 Issue 1 Pages 1-15
Published: 2012
Released on J-STAGE: December 16, 2014
JOURNAL OPEN ACCESSA polynomial that is nonnegative over a given domain T is called a positive polynomial. We consider the likelihood ratio test for the hypothesis of positivity that the estimand quadratic polynomial regression curve is a positive polynomial when T is the union of intervals. We define hierarchical hypotheses including the hypothesis of positivity, and derive their null distributions as mixtures of chi-square distributions. According to the volume-oftube method, the mixing probabilities are obtained through the evaluation of the volumes of boundaries of the closed convex cone K consisting of quadratic positive polynomials and its dual K*. We introduce the parameterizations of the boundaries of K and K*, and then provide expressions for the mixing probabilities. We demonstrate that the symmetric cone programming is useful for obtaining numerically the test statistics.View full abstractDownload PDF (763K) -
Toshio Shimokawa, Masashi GotoArticle type: Contributed Papers
2012 Volume 41 Issue 1 Pages 17-37
Published: 2012
Released on J-STAGE: December 16, 2014
JOURNAL OPEN ACCESSIn the medical field, accurate diagnosis of diseases is pivotal. The receiver operating characteristic (ROC) curve is a useful statistical graphic for evaluating laboratory test values in medical diagnosis. In recent years, some ROC curve methods and statistical inference methods based on the ROC curve have been proposed (e.g., Pepe, 1998: Wieand et al., 1989: Zou and Hall, 2000: Zweig and Campbell, 1993). However, few studies have identified the problem of the ROC curve regarding graphical representation. In this study, we consider this problem and develop three kinds of statistical graphics, namely, skill plot, likelihood ratio plot, and skillness plot. These plots were developed on the basis of power-normal distribution. The usefulness of these statistical graphics was evaluated using two practical examples. The results showed that our proposed graphics can overcome the problem of the ROC curve.View full abstractDownload PDF (1690K)
Notes
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Kunio TakezawaArticle type: Notes
2012 Volume 41 Issue 1 Pages 39-52
Published: 2012
Released on J-STAGE: December 16, 2014
JOURNAL OPEN ACCESSSimple regression using maximization of log likelihood in light of future data is attempted. Conventional maximum likelihood method is regarded as maximization of log likelihood in light of data at hand. Simple regression using maximization of log likelihood in light of future data gives a bias to the gradient. Extent of bias is yielded by the gradient given by least squares and the variance of the gradient. Use of this bias provides better regression equations than the conventional maximum likelihood method in terms of log likelihood in light of future data.View full abstractDownload PDF (674K) -
Takaharu Yamabe, Kazushi Maruo, Shingo Shirahata, Masashi GotoArticle type: Notes
2012 Volume 41 Issue 1 Pages 53-68
Published: 2012
Released on J-STAGE: December 16, 2014
JOURNAL OPEN ACCESSIn clinical trials, some measures of effect of ratio are used to evaluate the treatment effect between pre- and post-observed values of a drug. The most popular measure of effect of ratio is the percent change (PC), but symmetrized percent change (SPC) is sometimes applied in a trial. Some researchers examined the properties of two measures under the assumption of limited distribution for pre- and post-observed values, such as bivariate normal or bivariate log-normal distribution. In this paper, we evaluated the relationship between the variation of skewness of two measure (PC or SPC) and various shapes of pre- and post-observed data’s distribution, and evaluated the relationship between the statistical power and the variation of skewness of the two measures under the simultanious distribution of pre- and post-observed data following the bivariate power normal distribution. Then, we proposed how to apply the two measures in various situations.View full abstractDownload PDF (2803K)
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