多元方差分析在蚕桑方面的应用

本文应用多元方差分析对不同的桑品种、蚕品种的养蚕成绩（全茧量、茧层量）及制种成绩（造卵数、产卵数）进行分析,得到多倍体桑的制种成绩极显著地高于二倍体桑;三倍体桑饲养的苏５蚕品种的养蚕成绩为最佳的结论,为养蚕、制种生产提供了一定的理论依据     

Bayesian analysis of constant elasticity of variance models

This paper focuses on the estimation of some models in finance and in particular, in interest rates. We analyse discretized versions of the constant elasticity of variance (CEV) models where the normal law showing up in the usual discretization of the diffusion part is replaced by a range of heavy‐tailed distributions. A further extension of the model is to allow the elasticity of variance to be a parameter itself. This generalized model allows great flexibility in modelling and simplifies the model implementation considerably using the scale mixtures representation. The mixing parameters provide a means to identify possible outliers and protect inference by down‐weighting the distorting effects of these outliers. For parameter estimation, Bayesian approach is adopted and implemented using the software WinBUGS (Bayesian inference using Gibbs sampler). Results from a real data analysis show that an exponential power distribution with a random shape parameter, which is highly leptokurtic compared with the normal distribution, forms the best CEV model for the data. Copyright © 2006 John Wiley & Sons, Ltd.     

The Heston model with stochastic elasticity of variance

Empirical evidence suggests that single factor models would not capture the full dynamics of stochastic volatility such that a marked discrepancy between their predicted prices and market prices exists for certain ranges (deep in‐the‐money and out‐of‐the‐money) of time‐to‐maturities of options. On the other hand, there is an empirical reason to believe that volatility skew fluctuates randomly. Based upon the idea of combining stochastic volatility and stochastic skew, this paper incorporates stochastic elasticity of variance running on a fast timescale into the Heston stochastic volatility model. This multiscale and multifactor hybrid model keeps analytic tractability of the Heston model as much as possible, while it enhances capturing the complex nature of volatility and skew dynamics. Asymptotic analysis based on ergodic theory yields a closed form analytic formula for the approximate price of European vanilla options. Subsequently, the effect of adding the stochastic elasticity factor on top of the Heston model is demonstrated in terms of implied volatility surface. Copyright © 2016 John Wiley & Sons, Ltd.     

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.     

应用方差分析探讨影响电厂高速混床阻力大的主要因素

本文应用数理统计中的方差分析原理 ,对影响火力发电厂混床阻力大原因进行了数据分析和探讨 ,为改造设备、提高混床出水质量提供了可靠的论据。     

The generalized variance of a stationary autoregressive process

For a stationary autoregressive process of order p and disturbance variance σ² it is shown that the determinant of the covariance of T (≥p) consecutive random variables of the process is (σ²)^T Π_i,j=1^p (1 − w_iw_j)⁻¹, where w₁, …, w_p are the roots of the associated polynomial equation.     

New approach and analysis of the generalized constant elasticity of variance model

Generally, it is well known that the constant elasticity of variance (CEV) model fails to capture the empirical results verifying that the implied volatility of equity options displays smile and skew curves at the same time. In this study, to overcome the limitation of the CEV model, we introduce a new model, which is a generalization of the CEV model, and show that it can capture the smile and skew effects of implied volatility. Using an asymptotic analysis for two small parameters that determine the volatility shape, we obtain approximated solutions for option prices in the extended model. In addition, we demonstrate the stability of the solution for the expansion of the option price. Furthermore, we show the convergence rate of the solutions in Monte-Carlo simulation and compare our model with the CEV, Heston, and other extended stochastic volatility models to verify its flexibility and efficiency compared with these other models when fitting option data from the S&P 500 index.     

上市公司投资回报率的影响因素

影响证券投资者投资回报率的因素有很多，本文使用逐步回归方法从众多的因素中挑选出了对投资回报率有较大影响的因素，并建立了这些因素与投资回报率之间的数学模型。     

The asymptotic variance of a time average in a birth-death process

The variance of a time average is important for planning, running and interpreting experiments. This paper derives a simple method to find this variance for the case of a Markov process. This method is then applied to obtain the variance of a time average for the case of a birth-death process.     

One‐way analysis of variance with long memory errors and its application to stock return data

Recent empirical results indicate that many financial time series, including stock volatilities, often have long‐range dependencies. Comparing volatilities in stock returns is a crucial part of the risk management of stock investing. This paper proposes two test statistics for testing the equality of mean volatilities of stock returns using the analysis of variance (ANOVA) model with long memory errors. They are modified versions of the ordinary F statistic used in the ANOVA models with independently and identically distributed errors. One has a form of the ordinary F statistic multiplied by a correction factor, which reflects slowly decaying autocorrelations, that is, long‐range dependence. The other is a test statistic such that the degrees of freedom of the denominator in the ordinary F test statistic is calibrated by the so‐called effective sample size. Empirical sizes and powers of the proposed test statistics are examined via Monte Carlo simulation. An application to German stock returns is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Minimum variance estimators for misclassification probabilities in discriminant analysis

Let α(n₁, n₂) be the probability of classifying an observation from population Π₁ into population Π₂ using Fisher's linear discriminant function based on samples of size n₁ and n₂. A standard estimator of α, denoted by T₁, is the proportion of observations in the first sample misclassified by the discriminant function. A modification of T₁, denoted by T₂, is obtained by eliminating the observation being classified from the calculation of the discriminant function. The UMVU estimators, $\text{T}{}_1{}^1$ and $\text{T}{}_2{}^1$, of ET₁ = τ₁(n₁, n₂) and ET₂ = τ₂(n₁, n₂) = α(n₁ ? 1, n₂) are derived for the case when the populations have multivariate normal distributions with common dispersion matrix. It is shown that $\text{T}{}_1{}^1$ and $\text{T}{}_2{}^1$ are nonincreasing functions of D², the Mahalanobis sample distance. This result is used to derive the sampling distributions and moments of $\text{T}{}_1{}^1$ and $\text{T}{}_2{}^1$. It is also shown that α is a decreasing function of Δ² = (μ₁ ? μ₂)′Σ^?1(μ₁ ? μ₂). Hence, by truncating $\text{T}{}_1{}^1$ and $\text{T}{}_2{}^1$ (or any estimator) at the value of α for Σ = 0, new estimators are obtained which, for all samples, are as close or closer to α.     

拟因子试验设计在生产中的应用

根据生产实际,综合利用并列、赋闲列和拟水平试验设计,运用多重比较进行方差分析,寻找水泥熟料的最佳工艺.不仅解决了不同水平多因素试验问题,同时还可考虑交互作用,大大减少了试验次数,从而提高经济效益.     

平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.     

THE INEFFICIENCY OF LEASTSQUARES IN GAUSS-MARKOV ANDVARIANCE COMPONENT MODELS

1.IntroductionThispaperwillusethefollowingnotations.ForanymatrixA,A andW(A)denotetheMoors-PenroseinverseandthecolumnspaceofA,respectively.ForanysquarematrixA,IAImeansthedeterminantofA,A20(A>0)meansAisnonnegative(positive)definite.ConsidertheGauss-MarkovmodelY=Xo e,E(e)=0,Coy(e)~a'E,(1.1)whereYisann-dimensionalobservablerandomvector,XisannxpknownmatrixwithcolUInn-fUllrank,Tisapdimensionalparametervector,eisann-dimensionalunobserVablerandomvector,aZisanunknownpositiveparameter,Z20.I…     

Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model

This paper is concerned with the null distribution of test statistic T for testing a linear hypothesis in a linear model without assuming normal errors. The test statistic includes typical ANOVA test statistics. It is known that the null distribution of T converges to χ² when the sample size n is large under an adequate condition of the design matrix. We extend this result by obtaining an asymptotic expansion under general condition. Next, asymptotic expansions of one- and two-way test statistics are obtained by using this general one. Numerical accuracies are studied for some approximations of percent points and actual test sizes of T for two-way ANOVA test case based on the limiting distribution and an asymptotic expansion.     

非主观因素对小学生学习成绩影响的方差分析

本文采用非参数的方差分析方法,结合实际调查数据,初步探讨了性别、家庭类型、入学年龄等非主观因素对小学生学习成绩的影响。结果表明这些非主观因素对小学生的学习成绩是有显著影响的。     

On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored.     

Testing procedures for detection of linear dependencies in efficiency models

The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausmann-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.     

AN ANALYSIS OF AMULTIVARIATE TWO－WAY MODEL WITH INTERACTION AND NO REPLICATION

ＡＮＡＮＡＬＹＳＩＳＯＦＡＭＵＬＴＩＶＡＲＩＡＴＥＴＷＯ－ＷＡＹＭＯＤＥＬＷＩＴＨＩＮＴＥＲＡＣＴＩＯＮＡＮＤＮＯＲＥＰＬＩＣＡＴＩＯＮＧＵＯＤＡＷＥＩ（郭大伟）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉ...     

On upper bounds for the variance of functions of random variables

The upper bounds for the variance of a function g of a random variable X obtained in Cacoullos (1982) (for short CP) are improved in the case μ = E(X) ≠ 0. A main feature of these bounds is that they involve the second moment of the derivative or the difference of g. A multivariate extension for functions of independent random variables is also given.