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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Semiparametric adaptive estimation under informative samp...
Kosuke Morikawa, Yoshikazu Terada, Jae Kwang Kim · 2022-08-12 · via math.ST updates on arXiv.org

In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a well-known unbiased, consistent, and asymptotically normal estimator; however, it is not efficient. Thus, this study derives the semiparametric efficiency bound for various target parameters by considering the survey weight as a random variable and consequently proposes a semiparametric optimal estimator with certain working models on the survey weights. The proposed estimator is consistent, asymptotically normal, and efficient in a class of the regular and asymptotically linear estimators. Further, a limited simulation study is conducted to investigate the finite sample performance of the proposed method. The proposed method is applied to the 1999 Canadian Workplace and Employee Survey data.