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径向估计与球形性检验AI 解读

The first two moments for random symmetric matrices with radial distributions are given. This result enables one to generalize asymptotic procedures based on the sample covariance matrix to procedures based on a class of estimates for a positive-definite matrix parameter. This class includes the maximum likelihood estimates for the scatter matrix of an elliptical population, and affine-invariant robust estimates of a scatter matrix. Application of the results to the test for…

基于重叠数据的估计效率界AI 解读

If we have several estimates of the same quantity, based on partially overlapping sets of data, we can contemplate combining them, linearly, to give a single estimate. We give bounds, which depend only on the degrees of overlap but not on the individual variances, for the efficiency of the best linear unbiased combination of these estimates. with and without covariance information, relative to the overall best linear unbiased estimate. In particular, if the sets have no more…

逆高斯—泊松分布三种估计方法的渐近效率AI 解读

The two parameters of the inverse Gaussian-Poisson distribution may be estimated by (a) sample moments, (b) the proportion of zeros and the mean in the sample, and (c) by maximum likelihood. In the paper the asymptotic variances for all three joint estimation techniques and the corresponding efficiencies for methods (a) and (b) are derived. For θ ≥ 0.90 and α ≤ 1.5, the simple method (b) is highly efficient whereas the moment estimators are clearly inefficient. For 1.5 < α <…

高斯移动平均过程参数的最大似然估计AI 解读

Several authors have described methods for computing the exact maximum likelihood estimates for the parameters of a Gaussian moving average process. In this paper, an iterative procedure for solving the likelihood equations is derived which includes the covariance determinant. The procedure expresses the estimator of each parameter as a linear combination of a suitably large set of sample serial correlations which has many of the computational advantages of the direct…

四阶累积量谱密度积分的估计AI 解读

It is known that the asymptotic variance of a quasimaximum likelihood estimate for a non-Gaussian process contains certain integrals of the fourth order cumulant spectral density. If we apply the asymptotic theory we are required to estimate these integrals. Here we shall propose some operational consistent estimates for them.

位置M估计量的小样本渐近分布AI 解读

Asymptotic formulae for the distribution of M-estimators, i.e. maximum likelihood type estimators, of location, including the arithmetic mean, are derived which numerical studies show to give relative errors for densities and tail areas of the order of magnitude of 1% down to sample sizes 3 and 4 even in the extreme tails. The paper is the continuation of earlier work by the second author and is also closely related to Daniels's work on the saddlepoint approximation. The…

逻辑回归与判别分析中的惩罚极大似然估计AI 解读

Maximum likelihood estimation of the parameters of the binary logistic regression model for pr(H|x) is discussed with separate discussion of sampling from (i) the conditional distribution of H given x, (ii) the joint distribution of H and x, and (iii) the conditional distribution of x given H. Difficulties associated with continuous x in the latter sampling scheme are discussed. To avoid these, penalized maximum likelihood estimates are introduced, which give estimates of…

分段回归的一种新极大似然算法AI 解读

This paper presents a piecewise regression method for continuous models containing max or min operators, or both. This method does not require knowledge of the zone in which a shift in regimes occurs. Moreover, it allows the application of analytical derivatives to maximize the likelihood function, which greatly simplifies the estimation of the model. The method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables.

多个敏感属性的随机化回答技术AI 解读

Some randomized response techniques for investigating t ≧ 2 sensitive attributes are reviewed. A new technique is proposed that has the advantage of requiring only r trials per respondent (r ≦ t) if estimation of up to r-variate joint proportions is desired. The case of r = 2 is analyzed in detail. A procedure for deriving the restricted maximum likelihood estimators (MLE's) of the proportions and a test of independence between any set of pairs of attributes are given. The…

都市工资率的单因子多元时间序列模型AI 解读

The paper formulates and estimates a single-factor multivariate time series model. The model is a dynamic generalization of the multiple indicator (or factor analysis) model. It is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the Kalman filter algorithm. The model is used to obtain estimates of the unobserved metropolitan wage rate for Los Angeles, based on observations of sectoral wages within the…

二项分布参数 n 的估计AI 解读

Estimating the parameter n of the binomial distribution on the basis of r independent observations has been considered sporadically over the years. Many questions regarding asymptotic and small sample properties of moment, maximum likelihood, and related estimators either have been ignored or have received inadequate treatment. A unified and comprehensive study of these topics is given here. We also consider the problem of zero-truncated observations.

条件独立列联表中边际均值的统计推断AI 解读

Consider a three-way contingency table with factors A, B, and C. Assume factors A and B are independent for each given level of factor C. Inference procedures concerning the marginal means of the levels of factor A are studied. Maximum likelihood estimators, unbiased estimators, and uniformly minimum variance unbiased estimators are obtained. Exact variance formulas for the estimators are obtained. Large sample theory is developed and used for testing and confidence…

条件独立列联表中边际均值的推断AI 解读

Consider a three-way contingency table with factors A, B, and C. Assume factors A and B are independent for each given level of factor C. Inference procedures concerning the marginal means of the levels of factor A are studied. Maximum likelihood estimators, unbiased estimators, and uniformly minimum variance unbiased estimators are obtained. Exact variance formulas for the estimators are obtained. Large sample theory is developed and used for testing and confidence…

分段回归的一种新最大似然算法AI 解读

This paper presents a piecewise regression method for continuous models containing max or min operators, or both. This method does not require knowledge of the zone in which a shift in regimes occurs. Moreover, it allows the application of analytical derivatives to maximize the likelihood function, which greatly simplifies the estimation of the model. The method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables.

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二阶可容许性的充要条件及其在Berkson生物测定问题中的应用AI 解读

A theorem is proved which gives a necessary and sufficient condition for improving, up to $o(n^{-2})$, the mean squared error of the maximum likelihood estimate $\hat{\theta}$ by using an estimate of the form $\hat{\theta} + d(\hat{\theta})/n$. An application is made to a bioassay problem of Berkson.

可靠性分析中一类多项分布的最大似然估计AI 解读

Summary Let Xi, i = 1, …,k be independent Bernoulli variables, with Xi ~ B(1, pi). Let Y = σ Xi, and consider a multinomial experiment based on n independent, identically distributed observations Y 1,…, Yn. This model is identifiable in the ordered parameter vector (p (1),…, p (k)), where p(i -1) ≤ p(i), and arises in reliability experiments in which k components in parallel have potentially different probabilities of failure. The family of multinomial distributions with the…

使用分组数据估计回归模型的最大似然方法札记AI 解读

Summary The estimation of parameters for a class of regression models using grouped or censored data is considered. It is shown that with a simple reparameterization some commonly used distributions, such as the normal and extreme value, result in a log-likelihood which is concave with respect to the transformed parameters. Apart from its theoretical implications for the existence and uniqueness of maximum likelihood estimates, this result suggests minor changes to some…

最大似然估计与贝叶斯估计的一致性AI 解读

It is proved in the paper that every possible set of conditions which implies consistency of the maximum likelihood method also implies consistency of Bayes estimates for a large class of prior distributions. The method of the proof is based on a necessary and sufficient condition for the consistency of maximum likelihood estimates which is due to Perlman (1972). Perlman's result is improved as far as certain questions of measurability are concerned.

二项分布试验次数的估计方法比较AI 解读

Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution. Both the method of moments and the maximum likelihood estimators of n are considered. When p is unknown and small, while n is large, both estimators become highly unstable. Stabilized versions of these estimators are proposed, and their performance…

独立指数寿命下 k-out-of-m 系统可靠性估计量的近似均方误差AI 解读

Suppose S is a system with m independent components such that the system functions if and only if at least k components operate. Assume that the component lifetimes are identically exponentially distributed. This work provides simple approximation formulas for the mean squared errors of the minimum variance unbiased and the maximum likelihood estimators of reliability of this system. The performance of the proposed approximation formulas is investigated.

通过潜变量估计实现多指标多原因模型的 EM 方法AI 解读

This article considers both likelihood and Bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable. The model is complicated by its reduced form, which displays a mixture of econometric and psychometric themes. We avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form. This approach not only provides maximum likelihood estimates…