A Procedure for the Common Estimation of Parameters Corresponding to Several Treatment Groups

In this article we give a procedure for the common estimation of parameters corresponding to several treatment groups. Thereby we assume that the distribution functions of the groups belong to the same family and differ only in the parameter values. The procedure allows the common estimation of some of these parameters. The parameters themselves will be estimated by the maximum likelihood method; the estimators will be calculated iteratively by the Newton-Raphson method. To prove if the common estimation is possible, we propose as a suitable test the maximum likelihood ratio test. Finally we show the application of our procedure in the case of the probit analysis.     

Mixtures of Distributions by the Poisson Distribution of Order K

The Poisson-binomial, the Poisson-negative binomial (or Pascal) and Neyman's Type A distribution, which are Poisson mixtures of the binomial, the negative binomial and the Poisson distribution, respectively, have received a lot of attention in statistical literature [see e.g. Katti and Gurland (1961, 1962), Anscombe (1950), and Neyman (1939)]. In the present paper, their respective generalizations are introduced and briefly studied, when the Poisson distribution of order k [see Philippou (1983), Philippou, Georghiou and Philippou (1983), and Charalambides (1986)] replaces the Poisson distribution in its mixing role.     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.     

Estimation of Error Rates by Means of Simulated Bootstrap Distributions

The bootstrap error estimation method is investigated in comparison with the known π-method and with a combined error estimation suggested by us using simulated and normally distributed “populations” in 15 and 30 characters, respectively. For small sample sizes (below the double to threefold number of characters per class) the estimates resulting from the bootstrap method are on the average too small and can no longer be accepted. Significantly better results (with an essentially lower calculation expenditure) are obtained for the π-method and the combined estimation. The variability is essentially the same for all the three methods. This applies both in the case of rather badly separated and in the case of very well separated populations. A bootstrap estimation modified by us also gives unsatisfactory results.     

Estimation of Dynamic Rate Parameters in Insect Populations Undergoing Sublethal Exposure to Pesticides

With newer, more environmentally friendly and, subsequently less lethal, pesticides in use, evaluating efficacy of a pesticide now requires more than simply counting deaths after treatment. A discrete, age-structured matrix model that incorporates a species’ life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with an alternative continuous, age-structured model which offers significant advantage in considering sublethal damage. We use this continuous model to estimate time-dependent mortality parameters in an ordinary least-squares technique. Confidence intervals are given and results from tests for statistical significance of added parameters are presented.     

混合家系遗传参数估计方法研究

针对混合家系遗传参数估计,本文在假定公畜方差组分和母畜方差组分相等这一理论基础上,通过对方差分析的期望均方组成分析,提出了新的遗传力估计方法,以及某些特殊情况下的近似估计方法。通过一个估测实例比较了几种遗传力估计方法,结果表明,本文方法与全同胞组分估计最为接近,而且遗传力标准误最小,本文近似估计方法的效果也较好。对各种方法而言,资料越不平衡其差异越大。本文方法可以在一定程度上弥补全同胞分析时,因实际资料的公母畜方差组分差异过大的缺陷,具有实际可行性。此外,由于本文方法是用单因方差分析解决二因方差分析问题,计算更为简便,并可免于计算混合家系平均亲缘相关系数。     

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models

Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.     

湖羊出生类型与产活羔数表型及遗传参数估计

收集了26只湖羊种公羊115个女儿共计458窝产羔记录。统计分析表明,湖羊母羊胎产活羔数为1－5羔的比例分别为21．18％、49．78％、25．76％、3．06％和0．22％;公羊对母羊出生类型和产活羔数具有显著影响,胎次对母羊出生类型和产活羔数没有显著影响;母羊出生类型对其产活羔数没有显著影响;湖羊母羊出生类型与产活羔数的遗传力分别为0．251和0．097,它们之间的遗传、表型和环境相关分别为0．241、0．008和0．181,它们之间的协遗传力为0．038。这些参数表明：母羊出生类型与产活羔数是遗传联系不紧密的两个不同性状;根据母羊出生类型来早期选择产活羔数是无效的。     

多重二元响应Probit模型的渐近有效估计

针对多重二元响应Probit模型提出了两步估计方法,第一步由边际似然得到参数√n相合的估计,第二步通过一步迭代得到渐近有效估计,由于只需一步迭代,因此在利用模拟方法计算信息阵时,可以增加模拟的次数,从而减少模拟所产生的扰动对估计的影响．     

Estimation of random regression parameters

The problem of the best linear unbiased estimation (BLUE) of random regression parameters is considered. It is proved that increasing informations about the mean value of the parameters both extend the class of estimable linear functionals and improve on the estimation. In all investigated cases the uniqueness of BLUE is proved. In the case of known mean values the BLUE is shown to be numerically equivalent with the MMSEE almost everywhere. A numerical example shows the improvements of BLUE due to increasing informations about the mean values of the parameters.     

Estimation of Sheet Thickness Distributions from Linear and Plane Sections

A biological “membrane” or a “barrier” can often be modelled by a sheet, namely a portion of space comprised between two smooth, quasi-parallel faces, such that sheet thickness is in general variable but very small in relation to face extent. Sheet thickness measurements are often of interest to the morphometrist, the physiologist and the pathologist. In the present paper, some stereological techniques are developed for estimating true sheet thickness distributions, and their moments, from the apparent thickness or intercept length measurements obtained, respectively, via random plane or linear sections. An important premise for the models to work is that of isotropic random (‘non-preferential’) sheet orientation relative to the sectioning probe.     

Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

Estimation Problems in Fitting Genetic Models to Familial Data

Estimation of parameters in a genetic model can be very difficult using likelihood theory when there is no concise functional form for the likelihood function. An alternative method based on fitting the characteristic function is suggested and this method may be used on data with consistent familial composition.     

Scaleup in Suspension Crystallization of Two Multi Compound Fatty Acid Mixtures

Every vegetable oil needs specific process parameters for separation. These have to be determined in experiments for distinct scales and process parameters. Subsequently, fractionations of a mixture of 12 and a mixture of 8 fatty acids were carried out with the objective of producing a cloud point of 8 to 5 °C in the unsaturated product fraction. The data are used to present an improved version of a separation coefficient. The process is streamlined by reducing the crystallization steps to a minimum and decreasing the yield of the higher melting fractions. The filtration step was performed in different scales of the filter units to find the limits. To optimize the separation of fatty acid mixtures further an additional sweating procedure was applied. The following study highlights the scaleup in suspension crystallization of the examined materials and varied process parameters.     

Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-Negativity of Variance Estimators

For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.     

Logistic方程参数估计中的错误与修正

Logistic方程在种群生态学研究中被广泛应用,其积分式为N=k／（1＋e~（a-rt））,式中e~a=（k-N_0）／N_0。以往对该模型参数的各种估计方法,均将r,K和a作为三个相互独立的参数对待,而与e~a=（K-N_0）/N_0的假设相矛盾。由此估计出的参数K和a使实验初值N_0（t=0时的N值）发生偏离。笔者认为N_0是一个不带随机误差的常数,a值决定于K和N_0,而不是一个独立的参数,因而以往的参数估计方法是错误的,必须予以修正。本文提出了具体的修正方法,即用Marquardt方法或单纯形加速法求参数r和K,然后根据实验初值N_0求a,从而使Logistic微积分方程的共同参数r和K的估计一致。     

Maximum Likelihood Estimation of Simultaneous Pairwise Linear Structural Relationships

The problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem. Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re-analysing two data sets in the literature.     

Computational Algorithm for Least Squares Estimation of Parameters in Compartmental Analysis

This paper presents a new computational algorithm for the estimation of the parameters in multi-compartmental processes. By assuming the initial state of compartmental process known, the Newton-Raphson iterative process is vised to obtain weighted least squares estimates. The estimation procedure considers broad class of structural properties (defined in the sequel) of compartmental models, such as open-closed processes, cyclic pathways, conservative processes, connectivity etc. A computer program, which includes these structural properties is supplied. Two examples of simulated processes illustrate the estimation procedure.     

Estimation of Growth Norms from Incomplete Longitudinal Data

Longitudinal studies are rarely complete due to attrition, mistimed visits and observations missing at random. When the data are missing at random it is possible to estimate the primary location parameters of interest by constructing a modification of Zellner's (1962) seemingly unrelated regression estimator. Such a procedure is developed in this paper and is applied to a longitudinal study of coronary risk factors in children. The method consists of two stages in which the covariance matrix is estimated at the first stage. Using the estimated covariance matrix a generalized least squares estimator of the regression parameter vector is then determined at the second stage. Limitations of the procedure are also discussed.     

生物种群动态微分方程模型参数估计方法

本文以数值分析和最优化技术的有机结合为基础,提出了一种新的对动态微分方程模型直接进行数据拟合和参数估计方法,并以Logistic微分方程、生物种间竞争关系微分方程以及一种复合形态的Logistic微分方程为例进行了数据拟合试验．结果表明,该方法对各种动态微分方程模型均能进行最优拟合分析并求解其参数．同时发现,以前有的作者〔1,2,3,4,5〕提出的方法所得到的参数估计值存在系统误差且误差较大．