arXiv subjects

Junjun Lang

Publications and source records attributed to Junjun Lang.

3 recordsLinked to original sources

arXiv2026

Minimum Wasserstein distance estimator under covariate shift: closed-form, super-efficiency and irregularity

Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We propose a minimum Wasserstein distance estimation framework for inference under covariate shift that avoids explicit modeling of outcome regressions or importance weights. The resulting W-estimator admits a closed-form expression and is numerically equivalent to the classical 1-nearest neighbor estimator, yielding a new optimal transport interpretation of nearest neighbor methods. We establish root-$n$ asymptotic normality and show that the estimator is not asymptotically linear, leading to super-efficiency relative to the semiparametric efficient estimator under covariate shift in certain regimes, and uniformly in missing data problems. Numerical simulations, along with an analysis of a rainfall dataset, underscore the exceptional performance of our W-estimator.

stat.ME↗

arXiv2025

Unsupervised optimal deep transfer learning for classification under general conditional shift

Classifiers trained solely on labeled source data may yield misleading results when applied to unlabeled target data drawn from a different distribution. Transfer learning can rectify this by transferring knowledge from source to target data, but its effectiveness frequently relies on stringent assumptions, such as label shift. In this paper, we introduce a novel General Conditional Shift (GCS) assumption, which encompasses label shift as a special scenario. Under GCS, we demonstrate that both the target distribution and the shift function are identifiable. To estimate the conditional probabilities ${\bm\eta}_P$ for source data, we propose leveraging deep neural networks (DNNs). Subsequent to transferring the DNN estimator, we estimate the target label distribution ${\bm\pi}_Q$ utilizing a pseudo-maximum likelihood approach. Ultimately, by incorporating these estimates and circumventing the need to estimate the shift function, we construct our proposed Bayes classifier. We establish concentration bounds for our estimators of both ${\bm\eta}_P$ and ${\bm\pi}_Q$ in terms of the intrinsic dimension of ${\bm\eta}_P$ . Notably, our DNN-based classifier achieves the optimal minimax rate, up to a logarithmic factor. A key advantage of our method is its capacity to effectively combat the curse of dimensionality when ${\bm\eta}_P$ exhibits a low-dimensional structure. Numerical simulations, along with an analysis of an Alzheimer's disease dataset, underscore its exceptional performance.

math.ST↗

arXiv2024

Efficient estimation of partially linear additive Cox models and variance estimation under shape restrictions

Shape-restricted inferences have exhibited empirical success in various applications with survival data. However, certain works fall short in providing a rigorous theoretical justification and an easy-to-use variance estimator with theoretical guarantee. Motivated by Deng et al. (2023), this paper delves into an additive and shape-restricted partially linear Cox model for right-censored data, where each additive component satisfies a specific shape restriction, encompassing monotonic increasing/decreasing and convexity/concavity. We systematically investigate the consistencies and convergence rates of the shape-restricted maximum partial likelihood estimator (SMPLE) of all the underlying parameters. We further establish the aymptotic normality and semiparametric effiency of the SMPLE for the linear covariate shift. To estimate the asymptotic variance, we propose an innovative data-splitting variance estimation method that boasts exceptional versatility and broad applicability. Our simulation results and an analysis of the Rotterdam Breast Cancer dataset demonstrate that the SMPLE has comparable performance with the maximum likelihood estimator under the Cox model when the Cox model is correct, and outperforms the latter and Huang (1999)'s method when the Cox model is violated or the hazard is nonsmooth. Meanwhile, the proposed variance estimation method usually leads to reliable interval estimates based on the SMPLE and its competitors.

math.ST↗