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L1回归中的杠杆与崩溃AI 解读

In this article the notion of leverage of a design point when fitting a linear regression model is interpreted geometrically. In the case of least squares fitting, the leverage indicators based on the diagonal of the hat matrix are widely applied. By interpreting these hat matrix indicators geometrically, leverage can be generalized to groups of design points, as well as to other methods of fitting. The article introduces a leverage indicator that is appropriate for L 1…

若干二元符号检验与中位数的性质AI 解读

Brown and Hettmansperger proposed an affine invariant bivariate analogue of the sign test, the OS test, based on the generalized median of Oja. On the other hand, Oja and Nyblom introduced a family of locally most powerful affine invariant sign tests. In the case of elliptic distributions, the locally most powerful Blumen's test and the OS test are shown to be asymptotically equivalent. Formulas for calculating asymptotic relative efficiencies of the OS test and the Oja…

混合分布非参数极大似然估计的计算算法AI 解读

A fast algorithm for calculating the nonparametric maximum likelihood estimate (MLE) of a mixing distribution, G(·). in a mixture model is discussed. The literature contains several methods for computing the nonparametric MLE of G, but these methods are slow. In this article we develop an algorithm for maximizing the log-likelihood l(G) over the family ℊ, of all distribution functions, that yields the nonparametric MLE of G. In some semiparametric problems, a structural or…

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基于非对称极大似然的泊松过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

风险与生存分析中特定发生／暴露率的非参数估计AI 解读

A cohort of individuals exposed to some risk is followed up to a point of time M, and observations on two random variables (Y, Δ) are recorded for each individual. The variable Δ refers to one of the four possible events that can occur for an individual in the period [0, M]: (i) dies of a specific disease, say cancer, (ii) dies of a natural cause, (iii) withdraws from the study, and (iv) is alive and still under study at time M. The variable Y refers to the time at which an…

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比例风险模型的广义矩设定检验AI 解读

This article describes a generalized moments specification test of the semiparametric proportional hazards model of Cox. In contrast to other specification tests for this model, the generalized moments test is applicable in the presence of continuous explanatory variables and does not require assigning the data to predetermined cells. The results of a Monte Carlo investigation suggest that the generalized moments test has good finite-sample properties and that it is more…

接近最优值的回归平滑参数AI 解读

It is well known that data-driven regression smoothing parameters h based on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow as n-1/10; that is, for a bandwidth h0 optimizing the averaged squared error, n1/10 (h - h0)/h0 tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidths h0. This (nonrandom) smoothing…

含方差分量的非线性回归AI 解读

The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators,…

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基于非对称最大似然的 Poisson 过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

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家庭生育决策建模：非线性联立Probit模型AI 解读

This article proposes new methods for modeling household fertility decisions. Much of the demographic literature on this subject suggests that decisions relating to fertility are influenced by the orientations (attitudes, desires, intentions) of both husbands and wives, but the methods used in previous work do not indicate how wife's (husband's) orientation influences husband's (wife's) orientation, nor how these separate phenomena are combined to produce a joint decision.…

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平均导数估计的带宽选择AI 解读

The average derivative is the expected value of the derivative of a regression function. Kernel methods have been proposed as a means of estimating this quantity. The problem of bandwidth selection for these kernel estimators is addressed here. Asymptotic representations are found for the variance and squared bias. These are compared with each other to find an insightful representation for a bandwidth optimizing terms of lower order than n-1. It is interesting that, for…

人脑电偶极子参数的频域估计AI 解读

Human brain evoked potentials are elicited by a stimulus and can be recorded by scalp electrodes. Many researchers have proposed models in which evoked potentials are generated by equivalent electrical dipoles in the brain. Each dipole is defined by a set of parameters that specify its location, orientation, and magnitude. Existing approaches to estimation of dipole parameters do not realistically account for errors resulting from background brain electrical activity…

样条平滑参数的交叉验证与最大似然估计性能AI 解读

An important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter. In this article we report on an extensive simulation study that investigates the finite-sample performance of generalized cross-validation, cross-validation, and marginal likelihood estimators of the smoothing parameter in splines of orders 2 and 3. The performance criterion for both the estimate of the function and its first derivative is measured by the square…