Estimating conditional density functions is a fundamental problem in statistics.This task is crucial for understanding the underlying relationships between variables and for making informed predictions in various applications.In this paper, we introduce a novel deep nonparametric approach for estimating conditional density functions from data.Our method leverages the flexibility and expressiveness of deep neural networks to model the conditional density without imposing restrictive parametric assumptions.We formulate the problem of conditional density estimation as a nonparametric least squares problem, which allows us to harness the strengths of deep learning in a principled manner.By framing the problem this way, we can effectively utilize deep neural networks to approximate the conditional density function.We demonstrate that our proposed approach achieves the minimax optimal convergence rate for conditional density estimation.Additionally, we show that the convergence rate can be further improved for high-dimensional data satisfying a low-dimensional manifold assumption.To validate the performance of our approach, we conduct extensive numerical evaluations on both simulated and real-world datasets.These experiments reveal that our method consistently outperforms several established techniques, highlighting its superior accuracy and robustness in diverse scenarios.

Community network research has received extensive attention, and the study of dynamic random block networks is one of the emerging directions of network analysis.This paper first proposes a mixed membership autoregressive network model with a first-order autoregressive structure, then discusses the estimation of the membership matrix and community detection, and gives an AR-1 mixed spectral clustering algorithm for this model to estimate the membership matrix for community detection.In addition, an empirical eigenvalue threshold estimator is introduced to estimate the number of communities.Simulation results show that our method shows stronger generalization ability than previous methods for both random block community detection problems and mixed member community detection problems.Under different settings, the explicit error rate of our method does not exceed that of previous methods, and in many cases our method performs better.Application to real data proves the effectiveness of our method.

This paper addresses the challenge of detecting the change point in the covariance matrix of a high-dimensional random vector sequence.A novel reweighted CUSUM-type statistic is introduced, incorporating a data-adaptive parameter selection method to optimize weight determination.Building on this statistic, we develop a comprehensive framework for change point detection.Additionally, a hypothesis testing procedure is proposed to assess the existence of the change point based on our methodology.The study provides rigorous theoretical foundations for the proposed method, demonstrating the validity of parameter selection and the consistency of change point estimation.The effectiveness of the method is substantiated through extensive simulation studies and real-world data analysis, confirming its practical applicability and statistical reliability.

The baseline parametrization for two-level factorial designs has been receiving increasing attention recently.While the orthogonal parametrization is appropriate for experiments where the two levels of each factor are symmetrical, the baseline parametrization is well suited for experiments where the two levels of each factor are asymmetrical and one level, called a baseline level, is the default level.This paper considers a general situation where some factors have a baseline level while others do not.A mixed parametrization of factorial effects is proposed and its connection with the existing parametrizations is established.Under this new parametrization, we show that orthogonal arrays continue to be optimal for estimating main effects, and then put forward two minimum aberration criteria for further design selection.Both theoretical and algorithmic constructions of minimum aberration designs are examined and useful designs are obtained.

Technological advances have necessitated statistical methodologies for analyzing large-scale datastreams comprising multiple indefinitely time series. This manuscript proposes a dynamic tracking and screening (DTS) framework for online learning and model updating. Utilizing the sequential nature of datastreams, a robust estimation approach is developed under a linear varying coefficient model framework. This accommodates unequally-spaced design points and updates coefficient estimates without storing historical data. A data-driven choice of an optimal smoothing parameter is proposed, alongside a new multiple testing procedure for the streaming environment. Statistical guarantees of the procedure are provided, along with simulation studies on its finite-sample performance. The methods are demonstrated through a mobile health example estimating when subjects’ sleep and physical activities unusually influence their mood.

In this article, we consider change point inference for high dimensional linear models.For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression coefficients across the observations.Under some regularity conditions, the proposed new testing procedure controls the type I error asymptotically and is powerful against sparse alternatives and enjoys certain optimality.For change point identification, an "argmax" based change point estimator is proposed which is shown to be consistent for the true change point location.Moreover, combining with the binary segmentation technique, we further extend our new method for detecting and identifying multiple change points.Extensive numerical studies justify the validity of our new method and demonstrate its competitive performance.

The scalar-on-function regression is quite useful for modelling mixed-data in the context of scalar and functional variables.Under this class of regression, the paper aims at proposing a compelling alternative to model selection methods to address model selection uncertainty.The considered models characterize a scalar response using parametric effect of the scalar predictors and nonparametric effect of a functional predictor, and a model averaging estimation is developed based on Mallows-type criterion to assign weights for averaging.Further, the asymptotic optimality of the resulting estimator, in terms of achieving the smallest possible squared error loss, is established.Besides, simulation studies demonstrate its superiority to or comparability with some information criterion score-based model selection and averaging estimators.The proposed procedure is also applied to a mid-infrared spectra dataset for illustration.

The receiver operating characteristic (ROC) curve is frequently used to evaluate the accuracy of medical diagnostic tests.Currently, analysis based on the ROC curve has been performed in large public-use data arising from complex survey samples by ignoring the sampling scheme.This paper proposes a nonparametric estimator for the ROC curve that accounts for complex survey sampling.The asymptotic properties of the estimator are developed using empirical process arguments.Simulation studies showed that our proposed estimator performed well in the practical situations we considered, with better performance for larger sample size and disease proportions.The estimator was illustrated in the National Health and Nutrition Examination Survey (NHANES) to evaluate the discrimination of a traditional risk calculator of undiagnosed diabetes.

Two-sample multiple testing problems of sparse spatial data are frequently arising in a variety of scientific applications.In this article, we develop a novel neighborhood-assisted and posterior-adjusted (NAPA) approach to incorporate both the spatial smoothness and sparsity type side information to improve the power of the test while controlling the false discovery of multiple testing.We translate the side information into a set of weights to adjust the p-values, where the spatial pattern is encoded by the ordering of the locations, and the sparsity structure is encoded by a set of auxiliary covariates.We establish the theoretical properties of the proposed test, including the guaranteed power improvement over some stateof-the-art alternative tests, and the asymptotic false discovery control.We demonstrate the efficacy of the test through intensive simulations and two neuroimaging applications.

In this work, we extend the classical generalized functional linear model to a large-scale generalized functional linear model to handle a variety of complex situations where the response (possibly discrete) can be nonlinearly linked to an ultra-high number of functional predictors.Unlike most existing requirements on functional data, we don't need to impose any conditions regarding eigenvalue-decay or square-integrability on those functional predictors, resulting in a more flexible but challenging model framework.Based on a penalized model estimator, we develop a general inferential method to assess the significance of an arbitrary group of regression curves.Concretely, a pseudo score function is adopted to construct the associated confidence region for the regression curves of interest.Notably, the proposed test is justified uniformly convergent to nominal level, without any demand on estimation consistency of the regression curves.Finally, numerical studies are carried out to show the empirical performance of the proposed test.