两总体的逐步统计分辨数学模型及其应用

本文介绍了基于马氏准则下逐步统计分辨数学模型的基本原理 .对山东省胶南市 1 985～ 1 994年共 1 0年的第二代玉米螟百株累计卵量及其影响因素的历史观测数据资料进行了数量分析 ,建立了 4个逐步统计分辨数学模型 :Y1( X) =-4 2 .7655X1+0 .0 357X2 -2 .731 5X3Y2 ( X) =-2 7.74 58X1-0 .0 50 6X2 -2 .1 548X3Y3( X) =-62 .0 1 1 0 X1-0 .1 668X2 -2 .4 681 X3Y4 ( X) =-1 9.550 7X1-0 .0 94 0 X2 -1 .3831 X3运用这些模型 ,对历史资料进行回报验证 ,其历史符号率分别为 90 %、1 0 0 %、1 0 0 %、90 % .将 1 995、1 996两年观测数据作为独立样本进行试报 ,其预报结果与实际一致 .     

截尾正态分布的最小后验风险Bayes推断

设有两个总体G0、G1,分别服从参数为(μ0,σ)与(μ1,σ)的截尾正态分布.基于寿命数据X,考虑判别问题μ=μ0 vs.μ=μ1(μ1＞μ0＞0).本文依据最小后验风险准则,给出了上述问题的Bayes判决方法,为寿命判别制定了一个简便操作的规则.     

纠正一种用判别式求参数值的错误认识

“已知函数ｙ=2ｘ2 -ｋｘ 1 0ｘ2 4ｘ 6的最小值为 1 ,求实数ｋ的值”这是高中数学教学中常见的问题 .李素兰在 [1 ]中用判别式作出了它的详细解答 :由ｙ=2ｘ2 -ｋｘ 1 0ｘ2 4ｘ 6 可得(ｙ - 2 )ｘ2 (4ｙ ｋ)ｘ 6ｙ- 1 0 =0 .由题意△ =(4ｙ ｋ) 2 - 4(ｙ- 2 ) (6ｙ- 1 0 )≥ 0 .即 8ｙ2 - (8ｋ 88)ｙ 80 -ｋ2 ≤ 0 .因为　ｙ最小值 =1 ,所以　 1是方程 8ｙ2 - (8ｋ 88)ｙ 80 -ｋ2= 0的根 ,代入得ｋ2 8ｋ =0 .所以　ｋ=0或ｋ =- 8.[1 ]并认为 ,这是一种正确的解法 ,拙以为不妥 .纵观解题全过程 ,并不是每一推导过程都是可逆的 (例如…     

矩阵分裂比较定理的研究

本文利用分裂矩阵M.N的条件取代A~(-1)≥0或A~(-1)≥0,为实用提供了方便,首先提出相似非负矩阵和相似不等阵的概念,并用于拓广了矩阵分裂比较定理的.G.B.C.V条件.     

混合回归模型在百货商店市场细分中的应用

基于国内20家大型百货商店消费者满意调查数据,本文采用混合回归模型,对百货商店的消费者进行市场细分研究,发现百货商店的消费者可以分为6个差异化的细分市场.同时对每个细分市场的需求特征及市场规模进行了描述,并探讨了消费者人口统计变量与所属细分市场的关系.     

ZI纵向计数数据模型的影响分析

基于EM算法和Laplace逼近, 本文给出了研究ZI (即含0较多的)纵向计数数据模型的影响分析方法. 为了识别含0较多的分组计数数据中的强影响点, 本文将ZI纵向数据模型中取值为0的数据赋予一定的权重; 而把随机效应看作缺失数据; 在此基础上引入EM算法, 从而应用完全数据对数似然函数的条件期望以及相应的$Q$距离函数进行影响分析; 并进一步应用Laplace逼近方法简化EM算法中的积分计算. 在此基础上, 基于数据删除模型和局部影响分析方法导出了适用于ZI纵向计数数据模型的诊断统计量. 本文也通过实际计数数据的例子验证了诊断统计量的有效性.     

二元相依Weibu11分布的参数估计(英文)

考虑生存函数为F(x_1,x_2)=exp{-[(x_1~(1/α)/θ_1)~(1/δ) ((x_2~(1/α)/θ_2)~(1/δ)]~δ},x_i>0,θ_i>0,i=1,2,α>0,0<δ≤1的二无相依Weibull分布。基于在Ⅰ型截尾情形下两个元件与串联系统的寿命试验数据,本文给出了未知参数θ_1,θ_2,α和δ的估计,并讨论了这些估计的渐近性质。本文还给出了随机模拟的结果。     

一类新的广义割圆序列的线性复杂度及其自相关值

最近,丁存生基于新的割圆类(V_0,V_1)构造了循环码并研究了其性质.本文利用割圆类(V_0, V_1)构造了周期为pq的2阶二元序列,并计算了其自相关值、线性复杂度和极小多项式.     

基于逻辑斯缔映射的三参数混沌动力学系统的行为研究

基于逻辑斯缔映射的三参数混沌动力学系统为 xn+1=μxn(1 -xλn+c) .本文讨论了参数λ∈ (0 ,5 .2 ) ,μ∈ (0 ,1 2 .8) ,0 <|c| 1 .1 5 条件下该系统的行为特性 .在用计算机模拟 0 >c -1 .1 5 条件下该系统的行为时 ,发现了嵌入周期 1 轨道中的混沌动力学过程 .该过程显现出一种通向混沌的新途径 ,混沌区内部具有特殊的秩序结构     

一种更加省时的方差计算方法

<正>《中学生数学》2020年9月(下)文"置换平均数妙算方差"介绍了妙算方差的新方法,本文也介绍一种可以简化方差计算的方法.引例(1)先极端化考察,第一组数据2,2,2,2与第二组数据-1,-1,-1,-1,用定义或公式易得这两组数据的方差相等(都为0);(2)再变通考察,给出第一组数据4,7,9,     

Quantile regression with group lasso for classification

Applications of regression models for binary response are very common and models specific to these problems are widely used. Quantile regression for binary response data has recently attracted attention and regularized quantile regression methods have been proposed for high dimensional problems. When the predictors have a natural group structure, such as in the case of categorical predictors converted into dummy variables, then a group lasso penalty is used in regularized methods. In this paper, we present a Bayesian Gibbs sampling procedure to estimate the parameters of a quantile regression model under a group lasso penalty for classification problems with a binary response. Simulated and real data show a good performance of the proposed method in comparison to mean-based approaches and to quantile-based approaches which do not exploit the group structure of the predictors.     

Logistic biplot for nominal data

Classical biplot methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For binary data, logistic biplots have been recently developed. When data are nominal, both classical and binary logistic biplots are not adequate and techniques such as multiple correspondence analysis (MCA), latent trait analysis (LTA) or item response theory (IRT) for nominal items should be used instead. In this paper we extend the binary logistic biplot to nominal data. The resulting method is termed “nominal logistic biplot”(NLB), although the variables are represented as convex prediction regions rather than vectors. Using the methods from computational geometry, the set of prediction regions is converted to a set of points in such a way that the prediction for each individual is established by its closest “category point”. Then interpretation is based on distances rather than on projections. We study the geometry of such a representation and construct computational algorithms for the estimation of parameters and the calculation of prediction regions. Nominal logistic biplots extend both MCA and LTA in the sense that they give a graphical representation for LTA similar to the one obtained in MCA.     

A latent variables approach for clustering mixed binary and continuous variables within a Gaussian mixture model

For clustering objects, we often collect not only continuous variables, but binary attributes as well. This paper proposes a model-based clustering approach with mixed binary and continuous variables where each binary attribute is generated by a latent continuous variable that is dichotomized with a suitable threshold value, and where the scores of the latent variables are estimated from the binary data. In economics, such variables are called utility functions and the assumption is that the binary attributes (the presence or the absence of a public service or utility) are determined by low and high values of these functions. In genetics, the latent response is interpreted as the ??liability?? to develop a qualitative trait or phenotype. The estimated scores of the latent variables, together with the observed continuous ones, allow to use a multivariate Gaussian mixture model for clustering, instead of using a mixture of discrete and continuous distributions. After describing the method, this paper presents the results of both simulated and real-case data and compares the performances of the multivariate Gaussian mixture model and of a mixture of joint multivariate and multinomial distributions. Results show that the former model outperforms the mixture model for variables with different scales, both in terms of classification error rate and reproduction of the clusters means.     

A bayesian approach to binary response curve estimation

Summary The purpose of the present paper is to propose a practical procedure for the estimation of the binary response curve. The procedure is based on a model which approximates the response curve by a finely segmented piecewise constant function. To obtain a stable estimate we assume a prior distribution of the parameters of the model. The prior distribution has several parameters (hyper-parameters) which are chosen to minimize an information criterion ABIC. The procedure is applicable to data consisting of observations of a binary response variable and a single explanatory variable. The practical utility of the procedure is demonstrated by examples of applications to the dose response curve estimation, to the intensity function estimation of a point process and to the analysis of social survey data. The application of the procedure to the discriminant analysis is also briefly discussed. The Institute of statistical mathematics     

REML estimation for binary data in GLMMs

The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in mixed linear models. However, its extension to hierarchical generalized linear models (HGLMs) is often hampered by analytically intractable integrals. Numerical integration such as Gauss-Hermite quadrature (GHQ) is generally not recommended when the dimensionality of the integral is high. With binary data various extensions of the REML method have been suggested, but they have had unsatisfactory biases in estimation. In this paper we propose a statistically and computationally efficient REML procedure for the analysis of binary data, which is applicable over a wide class of models and design structures. We propose a bias-correction method for models such as binary matched pairs and discuss how the REML estimating equations for mixed linear models can be modified to implement more general models.     

Bayesian lasso binary quantile regression

In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Existing approaches to variable selection in a binary classification context are sensitive to outliers, heteroskedasticity or other anomalies of the latent response. The method proposed in this study overcomes these problems in an attractive and straightforward way. A Laplace likelihood and Laplace priors for the regression parameters are proposed and estimated with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A conceptional result is that by doing so, the binary regression model is moved from a Gaussian to a full Laplacian framework without sacrificing much computational efficiency. In addition, an efficient Gibbs sampler to estimate the model parameters is proposed that is superior to the Metropolis algorithm that is used in previous studies on Bayesian binary quantile regression. Both the simulation studies and the real data analysis indicate that the proposed method performs well in comparison to the other methods. Moreover, as the base model is binary quantile regression, a much more detailed insight in the effects of the covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is available in the R-package bayesQR.     

Analysis of correlated binary data under partially linear single-index logistic models

Clustered data arise commonly in practice and it is often of interest to estimate the mean response parameters as well as the association parameters. However, most research has been directed to address the mean response parameters with the association parameters relegated to a nuisance role. There is relatively little work concerning both the marginal and association structures, especially in the semiparametric framework. In this paper, our interest centers on the inference of both the marginal and association parameters. We develop a semiparametric method for clustered binary data and establish the theoretical results. The proposed methodology is investigated through various numerical studies.     

A bivariate finite mixture growth model with selection

Advances in Data Analysis and Classification - A model is proposed to analyze longitudinal data where two response variables are available, one of which is a binary indicator of selection and the...     

LOgistic响应分布中刻度参数的中、小样本推断

在火炸药产品的敏感性推断中，对响应分布的标准差给出较精确的推断，是基础性工作之一．为此，本文基于Logistic响应分布，在二元响应数据下，应用鞍点近似方法构造了刻度参数的近似置信区间，并进行了模拟研究．最后，本文将该方法应用于QD-8电雷管．模拟结果和实例分析表明，在中、小样本情形，本文方法对刻度参数的推断结果较为精确，显著改进了现行的基于渐近正态性的方法．