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厚切片 Wicksell 问题中的密度估计方法AI 解读

A new, implicit method is suggested for density estimation in inverse problems, where data are drawn not from the target distribution, but rather from its image under a transformation. The approach that we propose produces density estimators that are themselves densities, without the negativity problems known to plague more explicit inversion techniques. We also suggest a general empirical approach to selecting the smoothing parameter so as to optimize performance in the…

厚切片 Wicksell 问题的密度估计方法AI 解读

A new, implicit method is suggested for density estimation in inverse problems, where data are drawn not from the target distribution, but rather from its image under a transformation. The approach that we propose produces density estimators that are themselves densities, without the negativity problems known to plague more explicit inversion techniques. We also suggest a general empirical approach to selecting the smoothing parameter so as to optimize performance in the…

Maximum likelihood estimators for record-value data with a linear trend are quite sensitive to misspecification of the error distribution. Indeed, incorrect choice of that distribution can lead to inconsistent estimation of the intercept parameter and produce estimators of slope that do not enjoy the asymptotic convergence rate prescribed by the information matrix. These properties and the importance of linearly trended records lead us to suggest a distribution-free approach…

随机系数回归中截距与斜率分布的非参数估计AI 解读

An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric…

经验鞍点近似的性质AI 解读

SUMMARY The properties of the saddlepoint approximation are investigated when the required cumulant generating function is obtained empirically. Properties of the empirical moment generating function and empirical cumulant generating function and derivatives of these processes which are needed for this study are derived first, in particular their uniform consistency, moment structure, and weak convergence to normality are established. A numerical investigation exploring use…

经验特征函数方法的效率AI 解读

Summary The asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions.

用于统计推断的若干傅里叶方法AI 解读

Common statistical procedures such as maximum likelihood and M-estimation admit generalized representations in the Fourier domain. The Fourier domain provides fertile ground for approaching a number of difficult problems in inference. In particular, the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain…

天气干预试验的若干分析方法AI 解读

Using generalized densities, maximum likelihood and ancillarity, methods are developed for the analysis of randomized weather modification experiments that incorporate predictor variables. The linear logistic form is used to model the distributional singularity at the origin, while a gamma model with predictors is developed for the component conditional on the presence of precipitation. Connexions between the component submodels are explored and illustrated using an…

天气实验的若干分析方法AI 解读

Using generalized densities, maximum likelihood and ancillarity, methods are developed for the analysis of randomized weather modification experiments that incorporate predictor variables. The linear logistic form is used to model the distributional singularity at the origin, while a gamma model with predictors is developed for the component conditional on the presence of precipitation. Connexions between the component submodels are explored and illustrated using an…

经验特征函数及其应用AI 解读

Certain probability properties of $c_n(t)$, the empirical characteristic function $(\operatorname{ecf})$ are investigated. More specifically it is shown under some general restrictions that $c_n(t)$ converges uniformly almost surely to the population characteristic function $c(t).$ The weak convergence of $n^{\frac{1}{2}}(c_n(t) - c(t))$ to a Gaussian complex process is proved. It is suggested that the ecf may be a useful tool in numerous statistical problems. Application of…