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比例风险回归的函数型 ANOVA 建模AI 解读

The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one…

依赖数据密度估计中的带宽选择AI 解读

We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the "boundaries" that separate different modes of behaviour for…

风险率回归AI 解读

Linear splines and their tensor products are used to estimate the conditional log-hazard function based on possibly censored, positive response data and one or more covariates. An automatic procedure involving the maximum likelihood method, stepwise addition, stepwise deletion, and the Bayes Information Criterion is used to select the final model. The possible models contain proportional hazards models as a subclass, which makes it possible to diagnose departures from…

含变量测量误差的非参数回归AI 解读

The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel estimators. It is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution. In fact, there are two types of rates of convergence according to whether the error…

时间序列中的非参数函数估计AI 解读

Consider a stationary time series $(\mathbf{X}_t, Y_t), t = 0, \pm 1,\ldots,$ with $\mathbf{X}_t$ being $\mathbb{R}^d$-valued and $Y_t$ real-valued. The conditional mean function is given by $\theta(\mathbf{X}_0) = E(Y_0\mid\mathbf{X}_0)$. Under appropriate regularity conditions, a local average estimator of this function based on a finite realization $(\mathbf{X}_1, Y_1),\ldots,(\mathbf{X}_n, Y_n)$ can be chosen to achieve the optimal rate of convergence $n^{-1/(2 + d)}$ bot…

基于局部中位数的核估计量的渐近性质AI 解读

The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence $n^{-1/(2+d)}$ both pointwise and in the $L^q (1 \leq q < \infty)$ norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(2+d)}$ in the $L^\infty$ norm restricted to a…