Simultaneous confidence bands in spectral density estimation

We propose a method for the construction of simultaneous confidencebands for a smoothed version of the spectral density of a Gaussianprocess based on nonparametric kernel estimators obtained bysmoothing the periodogram. A studentized statistic is used todetermine the width of the band at each frequency and a frequency-domainbootstrap approach is employed to estimate the distributionof the supremum of this statistic over all frequencies. We proveby means of strong approximations that the bootstrap estimatesconsistently the distribution of the supremum deviation of interestand, consequently, that the proposed confidence bands achieveasymptotically the desired simultaneous coverage probability.The behaviour of our method in finite-sample situations is investigatedby simulations and a real-life data example demonstrates itsapplicability in time series analysis.     

Power for detecting genetic divergence: differences between statistical methods and marker loci

Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.     

A Modified Chi-Square Test for Testing Equality of Two Multinomial Populations Against an Ordering Restricted Alternative

A modified chi-square test for testing the equality of two multinomial populations against an ordering restricted alternative in one sample and two sample cases is constructed. The relation between a concept of dependence called dependence by chi-square and stochastic ordering is established. A tabulation of the asymptotic distribution of the test statistic under the null hypothesis is given. 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.     

Asymptotic Efficiency of the Chi-Square Test for Heterogeneity of Proportions in Some Sparse-Data Cases

We consider the problem of testing for heterogeneity of K proportions when K is not small and the binomial sample sizes may not be large. We assume that the binomial proportions are normally distributed with variance σ². The asymptotic relative efficiency (ARE) of the usual chi-square test is found relative to the likelihood-based tests for σ²=0. The chi-square test is found to have ARE = 1 when the binomial sample sizes are all equal and high relative efficiency for other cases. The efficiency is low only in cases where there is insufficient data to use the chi-square test.     

亚高寒草甸不同生境植物群落物种多度分布格局的拟合

物种多度分布是群落生态学研究的核心内容。通过对青藏高原东部亚高寒草甸3种不同生境草本植物群落的抽样调查,结合16个物种多度分布模型的两种曲线拟合优度检验得出如下结果：多种不同模型可以拟合同一生境的物种多度分布。相比于其他可拟合模型,几何级数模型在3种生境中两种拟合优度检验方法下的平均拟合效果是最好的,拟合优度值均在最优拟合优度值10左右波动。次优模型鉴于不同生境不同的检验方法表现不一。除了几何级数模型外,Sugihara分数模型在最小二乘法的拟合方法下,也可以拟合3种生境的物种多度分布。研究结果表明,仅用拟合优度检验区分产生不同物种分布格局的模型和机制是不可靠的,需要做进一步的检验性实验研究。