On the Reduction of Bias of Ratio Estimator to a Desired Degree

This paper advocates a procedure of obtaining an estimator (as a linear combination of a set of ratio estimators) whose bias can be reduced to a desired degree of sample size without any additional loss in efficiency.     

种群趋势指数的方差近似估计式及其应用

根据吴惠龙等（1986）发表的稻纵卷叶螟 Cnaphalocrocis medinalis 的生命表及 Watt 种群趋势指数数学模型,在delta-方法的基础上,本文提出了一种种群趋势指数方差的近似估计法,并应用于评价稻螟赤眼蜂Trichogramma japonicum Ashmead 及化学杀虫剂（甲六粉）对稻纵卷叶螟的控制作用。根据中心极限定律,当样本足够大时,种群趋势指数近似于正态分布。根据近似方差估计量以及 Z-检验方法,取得以下结论：放蜂区明显优于对照区,因其种群趋势指数取值较小,相应的 P 值为 0.0111,该区也明显优于化学杀虫剂处理区,相应的 P 值为 0.0036。杀虫剂处理区差于对照区,因其种群趋势指数值较大（0.3035）,但这种差异并未达到显著水平,P 值为 0.2236。虽然本文的结论近似于吴惠龙等（1986）单纯依据种群趋势指数所得到的结果,但本文的结论更具统计意义,更加可靠。     

Genetic heterogeneity of residual variance in broiler chickens

Aims were to estimate the extent of genetic heterogeneity in environmental variance. Data comprised 99 535 records of 35-day body weights from broiler chickens reared in a controlled environment. Residual variance within dam families was estimated using ASREML, after fitting fixed effects such as genetic groups and hatches, for each of 377 genetically contemporary sires with a large number of progeny (> 100 males or females each). Residual variance was computed separately for male and female offspring, and after correction for sampling, strong evidence for heterogeneity was found, the standard deviation between sires in within variance amounting to 15–18% of its mean. Reanalysis using log-transformed data gave similar results, and elimination of 2–3% of outlier data reduced the heterogeneity but it was still over 10%. The correlation between estimates for males and females was low, however. The correlation between sire effects on progeny mean and residual variance for body weight was small and negative (-0.1). Using a data set bigger than any yet presented and on a trait measurable in both sexes, this study has shown evidence for heterogeneity in the residual variance, which could not be explained by segregation of major genes unless very few determined the trait.     

Bounded rationality in volunteering public goods games

It is one of the fundamental problems in biology and social sciences how to maintain high levels of cooperation among selfish individuals. Theorists present an effective mechanism promoting cooperation by allowing for voluntary participation in public goods games. But Nash's theory predicts that no one can do better or worse than loners (players unwilling to join the public goods game) in the long run, and that the frequency of participants is independent of loners’ payoff. In this paper, we introduce a degree of rationality and investigate the model by means of an approximate best response dynamics. Our research shows that the payoffs of the loners have a significant effect in anonymous voluntary public goods games by this introduction and that the dynamics will drive the system to a fixed point, which is different from the Nash equilibrium. In addition, we also qualitatively explain the existing experimental results.     

An approximate likelihood estimator for the prevalence of infections in vectors using pools of varying sizes

There are several arthropods that can transmit disease to humans. To make inferences about the rate of infection of these arthropods, it is common to collect a large sample of vectors, divide them into groups (called pools), and apply a test to detect infection. This paper presents an approximate likelihood point estimator to rate of infection for pools of different sizes, when the variability of these sizes is small and the infection rate is low. The performance of this estimator was evaluated in four simulated scenarios, created from real experiments selected in the literature. The new estimator performed well in three of these scenarios. As expected, the new estimator performed poorly in the scenario with great variability in the size of the pools for some values of the parameter space.     

用近似熵测量神经放电峰峰间期的复杂性

近似熵是用来测量信号复杂程度的非线性方法。为了研究神经放电序列的复杂性,用该方法及其改进方法对大鼠损伤坐崩神经模型、大鼠脑薄片视上核神经元自发放电模型、背根节自发放电模型峰峰间期以及Rose-Hindmarsh理论神经元模型分叉数据进行了动态测量。结果表明,近似熵可以定量反映多种神经放电序列复杂性的变化,是一种较为有效的复杂性序量方法。     

The effect of epistasis on the excess of the additive and nonadditive variances after population bottlenecks

The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive x additive; VAD, additive x dominant; VDD; dominant x dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution alpha(i), which are equal to zero only for additive gene action within and between loci; and (2) the covariance between alpha2(i) and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V(NA) = V(D) + V(AA) + V(AD) + V(DD)) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V(A) and V(NA) was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V(A) and V(NA) was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V(A) over its ancestral value.     

Increased power with modified forms of the Levene (Med) test for heterogeneity of variance

While the conventional Levene (Med) test is a widely used and robust test for detecting heterogeneity of variance, it does not take notice of either the linear dependencies among the residuals involved or the possibility of a mean (or median)-variance relationship. This paper explores the substantial improvements in power possible by investigating the benefits both of removing such linear dependencies (structural zeros) and of modeling (even roughly) such relationships.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

方差分析在台木类木化石鉴定中的应用

本文用方差分析区别具台木类木材的三个种：太原台木(Dadoxylon taiyuanensis),生根无髓根（Amyelon radicans)和徐氏无髓根（A.xui),并同国外的种比较,结果表明,用这种方法能定量地研究植物性状之间的区别,并得到较好的效果。     

On the Application of the Analysis ct Variance in the Identification of Dadoxylon woods

This paper suggests that the analysis of variance could be used to the distinction of Da- doxylon-like woods and some quantitave characters of Dadoxylon taiyuanensis, Amyelon radicans, A. xui, A. equivius and Billigea resinosa, for example, diameter of ray cells and tracheids, height of rays, and diameter ratio of ray to tracheid, are compared and discussed. The comparision and discussion show quantitave character is more useful to identification of fossil plants than others if analysis Of variance is used.     

The Polynomial Model in the Multivariate Analysis of Variance

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy-coded or effect-coded design matrices) the so-called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.     

Stein's Two-Stage Test in Linear Models

After a brief presentation of Stein's two-sample test there is shown an improved procedure for general linear hypotheses analogous to the improvement of the two-sample-t-test described by Stein. The example of an analysis of variance in an one-way layout demonstrates the execution of the procedure as well as the problems that occur with the determination of the test parameters n₀ and z. For these problems there is finally suggested a practicable way of solution.     

生物实验数据的两因素方差分析

结合实例详细地叙述了生物实验数据的两因素方差分析计算方法,具有较强的实用意义。并介绍了如何分析计算结果。