A New STATISTIC FOR DETECTING INFLUENTIAL OBSERVATIONS IN A SCHEFFE' TYPE CALIBRATION CURVE

A statistic for identifying influential observations in calibration is given. The statistic is easy to interpret, and provides a useful measure of influence for Scheffé type calibration curves.     

Relations between statistics for testing exponentiality and uniformity

It is shown that Greenwood's statistic for uniformity and the Hahn-Shapiro and Stephens statistics for exponentiality with known origin are equivalent. It is also shown that the distribution of the Shapiro-Wilk statistic for testing the hypothesis of exponentiality with unknown origin is obtainable from the distribution of Greenwood's statistic.     

On testing correlation between growth curves

Fitting the growth curves by polynomials, this paper is intended to test whether or not there is any correlation between two characters. The likelihood ratio statistic is derived and is shown to be distributed under the null hypothesis as the product of three independent U statistics as defined in Anderson (1958). Box's procedure is then applied to approximate the critical region. A numerical example is given to illustrate the procedure.     

Comparison of efficient L- and R-estimators of location

Scholz (1974) proved that the asymptotic variance of an R-estimator of location is no larger than that of an L-estimator when the observations come from a distribution G different from the distribution F for which the two estimators are efficient. This note extends this result to distributions F whose density has a first but no second derivative.     

Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

It is important to detect the variance heterogeneity in regression model because efficient inference requires that heteroscedasticity is taken into consideration if it really exists. For the varying-coefficient partially linear regression models, however, the problem of detecting heteroscedasticity has received very little attention. In this paper, we present two classes of tests of heteroscedasticity for varying-coefficient partially linear regression models. The first test statistic is constructed based on the residuals, in which the error term is from a normal distribution. The second one is motivated by the idea that testing heteroscedasticity is equivalent to testing pseudo-residuals for a constant mean. Asymptotic normality is established with different rates corresponding to the null hypothesis of homoscedasticity and the alternative. Some Monte Carlo simulations are conducted to investigate the finite sample performance of the proposed tests. The test methodologies are illustrated with a real data set example.     

A Model Specification Test For GARCH(1,1) Processes

We provide a consistent specification test for generalized autoregressive conditional heteroscedastic (GARCH (1,1)) models based on a test statistic of Cramér‐von Mises type. Because the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model‐based (semiparametric) bootstrap method to approximate critical values of the test and to verify its asymptotic validity. Finally, we illuminate the finite sample behaviour of the test by some simulations.     

p-values for the Discrete Scan Statistic through Slack Variables

The discrete scan statistic is used in many areas of applied probability and statistics to study local clumping of patterns. Testing based on the statistic requires tail probabilities. Whereas the distribution has been studied extensively, most of the results are approximations, due to the difficulties associated with the computation. Results for exact p-values for the statistic have been given for a binary sequence that is independent or first-order Markovian. We give an algorithm to obtain probabilities for the statistic over multi-state trials that are Markovian of a general order of dependence, and explore the algorithm's usefulness.     

完善我国就业与失业统计指标体系的新方法

在我国,随着劳动力市场机制的运作及其功能的发挥,失业问题必然出现。因此,建立我国完整的就业与失业统计指标体系,对此进行反映、监测和分析,以采取及时有效的措施予以干预和控制,就有了非常重要的意义。     

Win statistics (win ratio,win odds,and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes

Conventional analyses of a composite of multiple time-to-event outcomes use the time to the first event. However, the first event may not be the most important outcome. To address this limitation, generalized pairwise comparisons and win statistics (win ratio, win odds, and net benefit) have become popular and have been applied to clinical trial practice. However, win ratio, win odds, and net benefit have typically been used separately. In this article, we examine the use of these three win statistics jointly for time-to-event outcomes. First, we explain the relation of point estimates and variances among the three win statistics, and the relation between the net benefit and the Mann–Whitney U statistic. Then we explain that the three win statistics are based on the same win proportions, and they test the same null hypothesis of equal win probabilities in two groups. We show theoretically that the Z-values of the corresponding statistical tests are approximately equal; therefore, the three win statistics provide very similar p-values and statistical powers. Finally, using simulation studies and data from a clinical trial, we demonstrate that, when there is no (or little) censoring, the three win statistics can complement one another to show the strength of the treatment effect. However, when the amount of censoring is not small, and without adjustment for censoring, the win odds and the net benefit may have an advantage for interpreting the treatment effect; with adjustment (e.g., IPCW adjustment) for censoring, the three win statistics can complement one another to show the strength of the treatment effect. For calculations we use the R package WINS, available on the CRAN (Comprehensive R Archive Network).