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序贯实验后的最优检验AI 解读

We develop methods for inference following sequential experiments by studying the asymptotic properties of tests. We find that the large-sample power of any test can be matched by a test in a suitable limit experiment involving Gaussian diffusions. This establishes that a fixed set of statistics are asymptotically sufficient for testing; these are the number of times each treatment has been sampled and the final value of the score/efficient influence function process for…

多臂老虎机实验中的风险与最优策略AI 解读

We provide a decision‐theoretic analysis of bandit experiments under local asymptotics. Working within the framework of diffusion processes, we define suitable notions of asymptotic Bayes and minimax risk for these experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a second‐order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds…

测量误差下的分布函数推断AI 解读

This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X=X∗+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗. We allow the density of ϵ to be ordinary or super smooth. We also provide…

存在变量测量误差的非参数工具变量回归AI 解读

This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for…

随机集合的经验似然AI 解读

In many statistical applications, the observed data take the form of sets rather than points. Examples include bracket data in survey analysis, tumor growth and rock grain images in morphology analysis, and noisy measurements on the support function of a convex set in medical imaging and robotic vision. Additionally, in studies of treatment effects, researchers often wish to conduct inference on nonparametric bounds for the effects which can be expressed by means of random…