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现代回归方法AI 解读

This new edition of Regression Methods has been updated and enhanced to include all-new information on the latest advances and research in the evolving field of regression analysis. It provides a unique treatment of fundamental regression methods, such as diagnostics, transformations, robust regression, and ridge regression. Unifying key concepts and procedures, this new edition emphasizes applications to provide a more hands-on and comprehensive understanding of regression…

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半参数部分样条与广义样条模型中的参数零模型检验AI 解读

Cox and Koh (1986) considered the model $y_i = f(x(i)) + \varepsilon_i, \varepsilon_i$ i.i.d. $N(0, \sigma^2)$, with the (parametric) null hypothesis $f(x), x \in \lbrack 0, 1 \rbrack$, a polynomial of degree $m - 1$ or less, versus the alternative $f$ is "smooth," based on the Bayesian model for $f$ which leads to polynomial smoothing spline estimates for $f$. They showed that there was no uniformly most powerful test and found the locally most powerful (LMP) test. We…

自助乘积极限过程的收敛速率AI 解读

We establish rates for strong approximations of the bootstrapped product-limit process and the corresponding quantile process. These results are used to show weak convergence of bootstrapped total time on test and Lorenz curve processes to the same limiting Gaussian processes as for the unbootstrapped versions. We develop fully nonparametric confidence bands and tests for these curves and apply these results to prostate cancer. We also present almost sure results for the…

广义线性模型中回归函数的自动平滑AI 解读

We consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models (Nelder and Wedderburn 1972) and present a generalized cross-validation procedure for empirically assessing an appropriate amount of smoothing in these estimates. Asymptotic arguments and numerical simulations are used to show that the generalized cross-validatory procedure preforms well from the point of view of a weighted mean squared error criterion.…

删失生存数据中风险率的非参数推断AI 解读

This paper concerns nonparametric inference for hazard rates with censored serial data. The focus is upon "delta sequence" estimators of the form $h_n(x) = \int K_b(x, y) dH_n(y)$ with $K_b$ integrating to 1 and concentrating mass near $x$ as $b \rightarrow 0. H_n$ is the Nelson-Aalen empirical cumulative hazard. Strong approximation and simultaneous confidence bands are derived for Rosenblatt-Parzen estimators, with $K_b(x, y) = w((x - y)/b)/b, b = o(n^{-1}),$ and $w(\cdot)$…