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1.
Two tests are derived for the hypothesis that the coefficients of variation of k normal populations are equal. The k samples may be of unequal size. The first test is the likelihood ratio test with the usual X2-approximation. A simulation study shows that the small sample behaviour under the null hypothesis is unsatisfactory. An alternative test, based on the sample coefficients of variation, appears to have somewhat better properties. 相似文献
2.
《Journal of Statistical Computation and Simulation》2012,82(18):3529-3543
ABSTRACTA frequently encountered statistical problem is to determine if the variability among k populations is heterogeneous. If the populations are measured using different scales, comparing variances may not be appropriate. In this case, comparing coefficient of variation (CV) can be used because CV is unitless. In this paper, a non-parametric test is introduced to test whether the CVs from k populations are different. With the assumption that the populations are independent normally distributed, the Miller test, Feltz and Miller test, saddlepoint-based test, log likelihood ratio test and the proposed simulated Bartlett-corrected log likelihood ratio test are derived. Simulation results show the extreme accuracy of the simulated Bartlett-corrected log likelihood ratio test if the model is correctly specified. If the model is mis-specified and the sample size is small, the proposed test still gives good results. However, with a mis-specified model and large sample size, the non-parametric test is recommended. 相似文献
3.
《Journal of Statistical Computation and Simulation》2012,82(9):1121-1130
A new generalized p-value method is proposed for testing the equality of coefficients of variation in k normal populations. Simulation studies show that the type I error probabilities are close to the nominal level. The proposed test is also compared with likelihood ratio test, modified Bennett's test and score test through Monte Carlo simulation, the results demonstrate that the generalized p-value method has satisfactory performance in terms of sizes and powers. 相似文献
4.
In the article, properties of the Bennett test and Miller test are analyzed. Assuming that the sample size is the same for each sample and considering the null hypothesis that the coefficients of variation for k populations are equal against the hypothesis that k ? 1 coefficients of variation are the same but differ from the coefficient of variation for the kth population, the empirical significance level and the power of the test are studied. Moreover, the dependence of the test statistic and the power of the test on the ratio of coefficients of variation are considered. The analyses are performed on simulated data. 相似文献
5.
The powers of the likelihood ratio (LR) test and an “asymptotically (in some sense) optimum” invariant test are examined and compared by simulation techniques with those of several other relevant tests for the problem of testing the equality of two univariate normal population means under the assumption of heterogeneous variances but homogeneous coefficients of variation. It is seen that the LR test is highly satisfactory for all values of the coefficient of variation and the “asymptotically optimum” invariant test, which is computationally much simpler than the LR test, is a reasonably good competitor for cases where the value of the coefficient of variation is greater than or equal to 3. Also, a 相似文献
6.
G. Edward Miller 《统计学通讯:模拟与计算》2013,42(2-3):743-750
A distribution-free test for the equality of the coefficients of variation from k populations is obtained by using the squared ranks test for variances, as presented by Conover and Iman (1978) and Conover (1980), on the original observations divided by their respective expected values. Substitution of the sample mean in place of the expected value results in the test being only asymptotically distribution-free. Results of a simulation study evaluating the size of the test for various coefficient of variation values and probability distributions are presented. 相似文献
7.
Robb J. Muirhead 《Revue canadienne de statistique》1982,10(1):59-62
It has recently been shown by Perlman (1980) that when testing the equality of several normal distributions it is the likelihood ratio test which is unbiased rather than a test based on a modified statistic in common use. This paper gives expansions for the null distribution of the likelihood ratio statistic as well as for the nonnull distribution in a special case. 相似文献
8.
《Journal of Statistical Computation and Simulation》2012,82(9):1686-1696
Paired binary data arise naturally when paired body parts are investigated in clinical trials. One of the widely used models for dealing with this kind of data is the equal correlation coefficients model. Before using this model, it is necessary to test whether the correlation coefficients in each group are actually equal. In this paper, three test statistics (likelihood ratio test, Wald-type test, and Score test) are derived for this purpose. The simulation results show that the Score test statistic maintains type I error rate and has satisfactory power, and therefore is recommended among the three methods. The likelihood ratio test is over conservative in most cases, and the Wald-type statistic is not robust with respect to empirical type I error. Three real examples, including a multi-centre Phase II double-blind placebo randomized controlled trial, are given to illustrate the three proposed test statistics. 相似文献
9.
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
10.
Broderick O. Oluyede 《统计学通讯:理论与方法》2013,42(4):1133-1155
A modified chi-square test for testing the equality of two multinomial populations against an order restricted alternative in one sample and two sample cases is constructed. The relation between the concepts of dependence by cM-square and stochastic ordering is established, The asymptotic distribution of the test statistic is the chi-bar-square type discussed by Robertson, Wright and Dykstra (1988). Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of the two multinomial populations. 相似文献
11.
Kun Chen 《统计学通讯:理论与方法》2019,48(10):2499-2508
Predicting asset prices is a critical issue in statistics and finance. In this article, by incorporating the recent advances in nonparametric approaches, we propose the empirical likelihood test for the predictability for the direction of price changes. Under some regularity conditions, the test statistic has an asymptotic χ2 distribution under the null hypothesis that the direction of price change cannot be predicted. This test procedure is easy to implement and presents better finite sample performances than other popular causality tests, as reported in some Monte Carlo experiments.
- Hightlights
We propose a non parametric likelihood test for predictability.
The test involves no user-chosen parameter or estimation of covariance matrix.
The test is simple to implement and has standard asymptotics.
The test has significantly better sizes than several popular tests with satisfactory power.
12.
S. R. Paul 《Revue canadienne de statistique》1989,17(2):217-227
We derive two C(α) statistics and the likelihood-ratio statistic for testing the equality of several correlation coefficients, from k ≥ 2 independent random samples from bivariate normal populations. The asymptotic relationship of the C(α) tests, the likelihood-ratio test, and a statistic based on the normality assumption of Fisher's Z-transform of the sample correlation coefficient is established. A comparative performance study, in terms of size and power, is then conducted by Monte Carlo simulations. The likelihood-ratio statistic is often too liberal, and the statistic based on Fisher's Z-transform is conservative. The performance of the two C(α) statistics is identical. They maintain significance level well and have almost the same power as the other statistics when empirically calculated critical values of the same size are used. The C(α) statistic based on a noniterative estimate of the common correlation coefficient (based on Fisher's Z-transform) is recommended. 相似文献
13.
In 1975, Lee and Gurland proposed a solution to the Behrens-Fisher problem. It had excellent control of size and power and was relatively simple to use. However it requires extensive special tables. This article proposes a modification of this approach. It replaces the tables with easily computed functions of the sample sizes and a standard t table. Control of size and power are equivalent to that obtained by Lee and Gurland. Furthermore, the test is also compared with the Welch's approximate t test and shows better control of size, with similar power curves when sample sizes are at least four from each of the two normal populations. 相似文献
14.
The statistical difference among massive data sets or signals is of interest to many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear curves, depending on spatial patterns, and have non-white noise that leads to difficulties in testing the significant differences between them. In this paper, we propose an adaptive Bayes sum test that can test the significance between two nonlinear curves by taking into account spatial dependence and by reducing the effect of non-white noise. Our approach is developed by adapting the Bayes sum test statistic by Hart [13]. The spatial pattern is treated through Fourier transformation. Resampling techniques are employed to construct the empirical distribution of test statistic to reduce the effect of non-white noise. A simulation study suggests that our approach performs better than the alternative method, the adaptive Neyman test by Fan and Lin [9]. The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations. 相似文献
15.
Yoshiko Isohgawa 《统计学通讯:理论与方法》2013,42(12):3521-3534
We consider the testing problems of the structural parameters for the multivariate linear functional relationship model. We treat the likelihood ratio test statistics and the test statistics based on the asymptotic distributions of the maximum likelihood estimators. We derive their asymptotic distributions under each null hypothesis respectively. A simulation study is made to evaluate how we can trust our asymptotic results when the sample size is rather small. 相似文献
16.
We consider the problem of hypothesis-testing under a logistic model with two dichotomous independent variables. In particular, we consider the case in which the coefficients β1, and β2 of these variables are known on an a priori basis to not be of opposite sign. For this situation we show that there exists a simple nonparametric altenative to the likelihood ratio test for testing H0: β1 = β2 = 0 VS.H1 at least one β1 = 0. We find the asympotic relative efficiency of this test and show that it exceeds 0.90 under a wide range of conditions. We also given an example. 相似文献
17.
Toshio Sakata 《统计学通讯:理论与方法》2013,42(11):3157-3168
The likelihood ratio test is derived for a one-sided hypothesis about the covariance matrices from two multivariate normal populations. In the case of equal sample sizes, the limiting distribution of -21og ?n is given, where ?n denotes the likelihood ratio criterion. When dimension p=2, for some alternatives, the power of -21og ?n of size 0.05 is compared with those of several well-known test statistics using Monte Carlo Methods. 相似文献
18.
We revisit the problem of testing homoscedasticity (or, equality of variances) of several normal populations which has applications in many statistical analyses, including design of experiments. The standard text books and widely used statistical packages propose a few popular tests including Bartlett's test, Levene's test and a few adjustments of the latter. Apparently, the popularity of these tests have been based on limited simulation study carried out a few decades ago. The traditional tests, including the classical likelihood ratio test (LRT), are asymptotic in nature, and hence do not perform well for small sample sizes. In this paper we propose a simple parametric bootstrap (PB) modification of the LRT, and compare it against the other popular tests as well as their PB versions in terms of size and power. Our comprehensive simulation study bursts some popularly held myths about the commonly used tests and sheds some new light on this important problem. Though most popular statistical software/packages suggest using Bartlette's test, Levene's test, or modified Levene's test among a few others, our extensive simulation study, carried out under both the normal model as well as several non-normal models clearly shows that a PB version of the modified Levene's test (which does not use the F-distribution cut-off point as its critical value), and Loh's exact test are the “best” performers in terms of overall size as well as power. 相似文献
19.
Many procedures exist for testing equality of means or medians to compare several independent distributions. However, the mean or median do not determine the entire distribution. In this article, we propose a new small-sample modification of the likelihood ratio test for testing the equality of the quantiles of several normal distributions. The merits of the proposed test are numerically compared with the existing tests—a generalized p-value method and likelihood ratio test—with respect to their sizes and powers. The simulation results demonstrate that proposed method is satisfactory; its actual size is very close to the nominal level. We illustrate these approaches using two real examples. 相似文献
20.
Using the concept of distributional distance, a test statistic is proposed FOR the hypothesis of independence in multidimensional contingency tables. A Monte Carlo Study is done to empirically compare the power of the proposed test to the Pearson x2 and the likelihood ratio test- Further, the nonnull distribution under various spike alternatives is tabulated 相似文献