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South Asian summer monsoon (SASM) delivers substantial rains to the Indian subcontinent and drives strong upwelling in the Arabian Sea, making marine upwelling records and terrestrial rainfall records two primary proxies for reconstructing past SASM variability. However, on orbital timescales, these two sets of records vary largely in opposite directions: the upwelling records are in-phase with Southern Hemisphere (SH) summer insolation, whereas the rainfall records are in-phase with Northern Hemisphere (NH) summer insolation. This leaves a long-standing debate on whether SASM is driven by NH or SH insolation. Here, combining paleoclimate records with transient climate simulations that explicitly separate the effects of the NH and SH insolation forcing, we show that the SASM rainfall is dominated by the NH insolation, whereas the Arabian Sea upwelling is forced predominantly by the SH insolation. When boreal summer occurs at perihelion, insolation is strongly enhanced not only in the NH but also in the tropical-subtropical SH. The former enhances the SASM rainfall through Eurasian warming, while the latter weakens the Arabian Sea upwelling by inducing South African warming and subsequent atmospheric teleconnections over the Indian Ocean. Our study reconciles the long-standing debate, and more broadly, reveals that warming in South Africa could exert a significant and previously overlooked remote forcing on the SASM system in past and future climate changes. 

Online nonparametric estimators are gaining popularity due to their efficient computation and competitive generalization abilities. An important example includes variants of stochastic gradient descent. These algorithms often take one sample point at a time and incrementally update the parameter estimate of interest. In this work, we consider model selection/hyperparameter tuning for such online algorithms. We propose a weighted rolling validation procedure, an online variant of leave-one-out cross-validation, that costs minimal extra computation for many typical stochastic gradient descent estimators and maintains their online nature. Similar to batch cross-validation, it can boost base estimators to achieve better heuristic performance and adaptive convergence rate. Our analysis is straightforward, relying mainly on some general statistical stability assumptions. The simulation study underscores the significance of diverging weights in practice and demonstrates its favorable sensitivity even when there is only a slim difference between candidate estimators. 

Modern data analysis and statistical learning are characterized by two defining features: complex data structures and black-box algorithms. The complexity of data structures arises from advanced data collection technologies and data-sharing infrastructures, such as imaging, remote sensing, wearable devices, and genomic sequencing. In parallel, black-box algorithms—particularly those stemming from advances in deep neural networks—have demonstrated remarkable success on modern datasets. This confluence of complex data and opaque models introduces new challenges for uncertainty quantification and statistical inference, a problem we refer to as ``black-box inference''. The difficulty of black-box inference lies in the absence of traditional parametric or nonparametric modeling assumptions, as well as the intractability of the algorithmic behavior underlying many modern estimators. These factors make it difficult to precisely characterize the sampling distribution of estimation errors. A common approach to address this issue is post-hoc randomization, which includes permutation, resampling, sample splitting, cross-validation, and noise injection. When combined with mild assumptions, such as exchangeability in the data-generating process, these methods can yield valid inference and uncertainty quantification. Post-hoc randomization methods have a rich history, ranging from classical techniques like permutation tests, the jackknife, and the bootstrap, to more recent developments such as conformal inference. These approaches typically require minimal knowledge about the underlying data distribution or the inner workings of the estimation procedure. While originally designed for varied purposes, many of these techniques rely, either implicitly or explicitly, on the assumption that the estimation procedure behaves similarly under small perturbations to the data. This idea, now formalized under the concept of \emph{stability}, has become a foundational principle in modern data science. Over the past few decades, stability has emerged as a central research focus in both statistics and machine learning, playing critical roles in areas such as generalization error, data privacy, and adaptive inference. In this article, we investigate one of the most widely used resampling techniques for model comparison and evaluation---cross-validation (CV)---through the lens of stability. We begin by reviewing recent theoretical developments in CV for generalization error estimation and model selection under stability assumptions. We then explore more refined results concerning uncertainty quantification for CV-based risk estimates. By integrating these research directions, we uncover new theoretical insights and methodological tools. Finally, we illustrate their utility across both classical and contemporary topics, including model selection, selective inference, and conformal prediction. 

Abstract In some high-dimensional and semiparametric inference problems involving two populations, the parameter of interest can be characterized by two-sample U-statistics involving some nuisance parameters. In this work we first extend the framework of one-step estimation with cross-fitting to two-sample U-statistics, showing that using an orthogonalized influence function can effectively remove the first order bias, resulting in asymptotically normal estimates of the parameter of interest. As an example, we apply this method and theory to the problem of testing two-sample conditional distributions, also known as strong ignorability. When combined with a conformal-based rank-sum test, we discover that the nuisance parameters can be divided into two categories, where in one category the nuisance estimation accuracy does not affect the testing validity, whereas in the other the nuisance estimation accuracy must satisfy the usual requirement for the test to be valid. We believe these findings provide further insights into and enhance the conformal inference toolbox. 

Speleothem δ18O records from central southern China have long been regarded as a key benchmark for Asian summer monsoon intensity. However, the similar δ18O minima observed among precession minima and their link to seasonal precipitation mixing remains unclear. Here, we present a 400,000-y record of summer precipitation δ18O from loess microcodium, which captures distinct precession cycles similar to those seen in speleothem δ18O records, particularly during glacial periods. Notably, our microcodium δ¹⁸O record reveals very low-δ¹⁸O values during precession minima at peak interglacials, a feature absent in speleothem δ¹⁸O records from central southern China. This discrepancy suggests that the mixed summer and nonsummer climatic signals substantially influence the speleothem δ¹⁸O records from central southern China. Proxy-model comparisons indicate that the lack of very low-δ¹⁸O values in speleothem δ¹⁸O records is due to an attenuated summer signal contribution, resulting from a lower summer-to-annual precipitation ratio in southern China at strong monsoon intervals. Our findings offer a potential explanation for the long-standing puzzle of the absence of 100- and 41-kyr cycles in speleothem δ¹⁸O records and underscore the critical role of seasonality in interpreting paleoclimatic proxies in central southern China. These insights also have broader implications for interpreting speleothem δ¹⁸O records globally, advocating for a more multiseason interpretive framework. 

ABSTRACT In genomics studies, the investigation of gene relationships often brings important biological insights. Currently, the large heterogeneous datasets impose new challenges for statisticians because gene relationships are often local. They change from one sample point to another, may only exist in a subset of the sample, and can be nonlinear or even nonmonotone. Most previous dependence measures do not specifically target local dependence relationships, and the ones that do are computationally costly. In this paper, we explore a state-of-the-art network estimation technique that characterizes gene relationships at the single cell level, under the name of cell-specific gene networks. We first show that averaging the cell-specific gene relationship over a population gives a novel univariate dependence measure, the averaged Local Density Gap (aLDG), that accumulates local dependence and can detect any nonlinear, nonmonotone relationship. Together with a consistent nonparametric estimator, we establish its robustness on both the population and empirical levels. Then, we show that averaging the cell-specific gene relationship over mini-batches determined by some external structure information (eg, spatial or temporal factor) better highlights meaningful local structure change points. We explore the application of aLDG and its minibatch variant in many scenarios, including pairwise gene relationship estimation, bifurcating point detection in cell trajectory, and spatial transcriptomics structure visualization. Both simulations and real data analysis show that aLDG outperforms existing ones.