TY - JOUR

T1 - Homogeneity tests for several Poisson populations

AU - Chiu, Sung Nok

AU - Wang, Ling

N1 - We thank the referees for their helpful suggestions, especially for suggesting the use of graphical instead of tabular presentations. This research was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project Numbers HKBU200605 and HKBU200807) and an FRG grant of the Hong Kong Baptist University.

PY - 2009/10

Y1 - 2009/10

N2 - In this paper we compare the size distortions and powers for Pearson's χ2-statistic, likelihood ratio statistic L R, score statistic S C and two statistics, which we call U T and V T here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183-190] for testing the equality of the rates of K Poisson processes. Asymptotic tests and parametric bootstrap tests are considered. It is found that the asymptotic U T test is too conservative to be recommended, while the other four asymptotic tests perform similarly and their powers are close to those of their parametric bootstrap counterparts when the observed counts are large enough. When the observed counts are not large, Monte Carlo simulation suggested that the asymptotic test using S C, L R and U T statistics are discouraged; none of the parametric bootstrap tests with the five statistics considered here is uniformly best or worst, and the asymptotic tests using Pearson's χ2 and V T always have similar powers to their bootstrap counterparts. Thus, the asymptotic Pearson's χ2 and V T tests have an advantage over all five parametric bootstrap tests in terms of their computational simplicity and convenience, and over the other four asymptotic tests in terms of their powers and size distortions.

AB - In this paper we compare the size distortions and powers for Pearson's χ2-statistic, likelihood ratio statistic L R, score statistic S C and two statistics, which we call U T and V T here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183-190] for testing the equality of the rates of K Poisson processes. Asymptotic tests and parametric bootstrap tests are considered. It is found that the asymptotic U T test is too conservative to be recommended, while the other four asymptotic tests perform similarly and their powers are close to those of their parametric bootstrap counterparts when the observed counts are large enough. When the observed counts are not large, Monte Carlo simulation suggested that the asymptotic test using S C, L R and U T statistics are discouraged; none of the parametric bootstrap tests with the five statistics considered here is uniformly best or worst, and the asymptotic tests using Pearson's χ2 and V T always have similar powers to their bootstrap counterparts. Thus, the asymptotic Pearson's χ2 and V T tests have an advantage over all five parametric bootstrap tests in terms of their computational simplicity and convenience, and over the other four asymptotic tests in terms of their powers and size distortions.

UR - http://www.scopus.com/inward/record.url?scp=69449089426&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2009.05.017

DO - 10.1016/j.csda.2009.05.017

M3 - Journal article

AN - SCOPUS:69449089426

SN - 0167-9473

VL - 53

SP - 4266

EP - 4278

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 12

ER -