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传染病传播模型中接触率的最小二乘估计AI 解读

The contact rate and associated contact number determine the rate of spread of an infectious disease whose population dynamics are described by a mathematical model. It is shown how to obtain least-squares estimates of the contact rate for a standard homogeneous univariate model and a four-group model with different contact rates between the groups. The results of a small scale simulation are presented in the case of the four-group model. It is argued that the least-squares…

传染病传播模型中接触率的最小二乘估计AI 解读

The contact rate and associated contact number determine the rate of spread of an infectious disease whose population dynamics are described by a mathematical model. It is shown how to obtain least-squares estimates of the contact rate for a standard homogeneous univariate model and a four-group model with different contact rates between the groups. The results of a small scale simulation are presented in the case of the four-group model. It is argued that the least-squares…

对称性检验AI 解读

We introduce the characteristic symmetry function, based on the characteristic function of the underlying distribution, whose behaviour is indicative of symmetry or its absence. A statistic is proposed for testing symmetry about an unspecified centre, derived from the empirical characteristic symmetry function. The statistic is readily computible, it utilizes information in the empirical characteristic function over an interval, and does not require the estimation of the…

模型误设下位置与尺度参数的最小均方距离估计AI 解读

The paper is concerned with estimating location and scale parameters by estimators minimizing a mean squared distance between the empirical distribution function and a conveniently chosen parameterized distribution function. Within the true parametric family the location estimator has the same asymptotic distribution as that of Hodges & Lehmann. If the underlying distribution is not a member of the assumed parametric family, the questions concerning bias, rather than…

线性回归中斜率的估计与异常值识别AI 解读

The paper presents a large sample method for estimating the slope parameter in a linear model by minimizing a loss function related to the empirical cumulant generating function of the error distribution. A family of estimators, indexed by a real parameter, is obtained and consistency and asymptotic normality established. The optimum member of the family is that which has minimum variance with respect to the parameter. This minimization together with a characterization…

线性回归中的斜率估计与异常值识别AI 解读

The paper presents a large sample method for estimating the slope parameter in a linear model by minimizing a loss function related to the empirical cumulant generating function of the error distribution. A family of estimators, indexed by a real parameter, is obtained and consistency and asymptotic normality established. The optimum member of the family is that which has minimum variance with respect to the parameter. This minimization together with a characterization…

参数的积分平方误差估计AI 解读

The paper develops in a more general setting the methods used by Paulson, Holcomb & Leitoh (1976) to estimate the parameters of a stable law. The statistic considered minimizes a distance function determined by the empirical characteristic function. Consistency is established under the condition of differentiability of the characteristic function and the existence of bounded second derivatives is required to obtain a central limit theorem for the estimators of one or more…

参数的积分平方误差估计AI 解读

The paper develops in a more general setting the methods used by Paulson, Holcomb & Leitoh (1976) to estimate the parameters of a stable law. The statistic considered minimizes a distance function determined by the empirical characteristic function. Consistency is established under the condition of differentiability of the characteristic function and the existence of bounded second derivatives is required to obtain a central limit theorem for the estimators of one or more…

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连续时间随机游走及其在排队理论中的应用AI 解读

The random walk in continuous time has been considered by a number of authors for particular types of boundary conditions, e. g. the unrestricted random walk by Irwin (1937); the random walk with one absorbing or one reflecting barrier by Ledermann & Reuter (1954), and subsequently by Bailey (1954). The present paper gives a unified theory of these processes which includes previous work on the subject as special cases and readily yields the solution for any other consistent…