On an Auxiliary Function for Log-Density Estimation

非迭代似然导出估计：通过辅助估计方程

Noniterative Likelihood-Derived Estimation through Auxiliary Estimating Equations

本文提出一种通过辅助估计方程构造非迭代似然导出估计量的方法，得到闭式估计量，并建立其理论性质，通过多种模型和模拟验证了其有效性。

Debiased Machine Learning without Sample-Splitting for Stable Estimators

Estimation and inference on causal parameters is typically reduced to a generalized method of moments problem, which involves auxiliary functions that correspond to solutions to a regression or classification problem. Recent line of work on debiased machine learning shows how one can use generic machine learning estimators for these auxiliary problems, while maintaining asymptotic normality and root-$n$ consistency of the target parameter of interest, while only requiring mean-squared-error guarantees from the auxiliary estimation algorithms. The literature typically requires that these auxili…

尺度依赖于辅助变量的非参数回归

Nonparametric regression with the scale depending on auxiliary variable

研究了在均数积分平方误差（MISE）准则下异方差非参数多元回归中单变量分量的估计问题。目的是了解尺度函数应如何用于单变量分量的估计。它是已知的，尺度函数不影响MISE收敛的速度，并作为一个结果尖锐的常数进行了探索。本文首先发展了一个关键模型$Y=f(X)+σ(X,\mathbf{Z})\varepsilon$的sharp-minimax理论，其中$\varepsilon$是标准正态的，并且独立于预测变量X和辅助向量协变量$\mathbf{Z}$。证明了如果尺度$σ(x,\mathbf{z})$依赖于辅助变量，则利用尺度（或其估计）的一个特殊估计量是渐近尖锐的minimax，并且对f（x）的未知光滑性是自适应的.这是一个有趣的结论，因为如果尺度不依赖于辅助协变量$\mathbf{Z}$，则忽略异方差可以产生尖锐的极小极大估计。枢轴模型作为一般加法模型$Y=f(X)+g(\mathbf{Z})+σ(X,\mathbf{Z})\varepsilon$的自然基准，其中$\varepsilon$可以依赖于$(X,\mathbf{Z})$并且只有有限的四阶矩。它表明，对于这个模型的数据驱动的估计可以执行以及基准。此外，估计，建议连续响应，也可以用于离散响应的情况下。伯努利和泊松回归，这是固有的异方差，是特别考虑的例子，其中尖锐的极大极小下界，以及获得。数值研究表明，渐近理论揭示了小样本。

Nonparametric Estimation of Conditional Expectation with Auxiliary Information and Dimension Reduction

Nonparametric estimation of the conditional expectation $E(Y | U)$ of an outcome $Y$ given a covariate vector $U$ is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable $Z$ in the training dataset used to construct estimators, but $Z$ is not available for future prediction or selecting patient treatment in personalized medicine. For example, in the training dataset longitudinal outcomes are observed, but only the last outcome $Y$ is concerned in the future prediction or analysis. The lo…

Log-logistic和韦布尔分布最小二乘回归估计权系数的精确表达式

Exact expressions for the weights used in least-squares regression estimation for the log-logistic and Weibull distribution

对数逻辑分布和韦布尔分布的估计可使用概率绘图所用的方程进行。该方程导致高度异方差回归。推导出残差方差的精确表达式，可用于进行加权回归。在大样本情况下，最大似然估计的性能最好，但在小样本情况下，加权回归在偏差和均方误差方面优于极大似然估计。

一种惩罚逻辑广义回归估计量

A penalized logistic generalized regression estimator

本文在模型辅助框架下提出一种惩罚逻辑广义回归估计量，结合Lasso或Ridge惩罚控制辅助变量影响，经模拟和实例验证可提高稀疏模型下估计效率，适用于含多辅助变量的复杂调查数据场景。

Auxiliary Quantile Forecasting with Linear Networks

We propose a novel multi-task method for quantile forecasting with shared Linear layers. Our method is based on the Implicit quantile learning approach, where samples from the Uniform distribution $\mathcal{U}(0, 1)$ are reparameterized to quantile values of the target distribution. We combine the implicit quantile and input time series representations to directly forecast multiple quantile estimations for multiple horizons jointly. Prior works have adopted a Linear layer for the direct estimation of all forecasting horizons in a multi-task learning setup. We show that following similar intuit…

非正态化统计模型的一族计算有效且简单的估计

A Family of Computationally Efficient and Simple Estimators for Unnormalized Statistical Models

我们引入了一个新的家庭的非正规化统计模型的估计。我们的估计族由两个非线性函数参数化，并使用来自辅助分布的单个样本，推广了Geyer和Thompson（1992）的最大似然Monte Carlo估计。该族使得我们可以像估计模型中的任何其他参数一样估计配分函数。通过优化一个代数上简单的、定义明确的目标函数来完成估计，这允许使用专用的优化方法。我们建立了估计族的一致性，并给出了渐近协方差矩阵的表达式，这使我们能够进一步分析非线性和辅助密度对估计性能的影响。在我们的家庭中的一些估计是特别稳定的辅助密度范围很广。有趣的是，非线性的特定选择建立了密度估计和非线性逻辑回归分类之间的联系。最后，从计算效率的角度考虑了相对于给定数据量的辅助样本的最佳数量。

具有结构化协方差矩阵的线性模型中带辅助尺度的多元MM估计量

Multivariate MM-estimators with auxiliary Scale for Linear Models with Structured Covariance Matrices

本文提出一种统一的带辅助尺度的MM估计方法，用于具有结构化协方差矩阵的平衡线性模型，证明其兼具高稳健性和高效率，并建立了存在性、渐近性质及崩溃点和影响函数等稳健性理论。

Nonparametric imputation method for nonresponse in surveys

Many imputation methods are based on statistical models that assume that the variable of interest is a noisy observation of a function of the auxiliary variables or covariates. Misspecification of this model may lead to severe errors in estimates and to misleading conclusions. A new imputation method for item nonresponse in surveys is proposed based on a nonparametric estimation of the functional dependence between the variable of interest and the auxiliary variables. We consider the use of smoothing spline estimation within an additive model framework to flexibly build an imputation model in …

内生函数线性回归中弱或无关辅助变量下的识别稳健检验

Identification-Robust Testing in Endogenous Functional Linear Regression with Weak or Irrelevant Auxiliary Variables

针对函数线性回归中斜率函数的检验问题，提出基于辅助变量函数矩条件的无降维检验方法，在弱甚至无关辅助变量下仍保持渐近有效性，并建立了渐近分布理论。

MTCNET: 用于人群计数估计的多任务学习范式

MTCNET: Multi-task Learning Paradigm for Crowd Count Estimation

针对人群计数因尺度变化和视角问题的挑战，提出MTCNet多任务学习架构，以密度估计为主任务、计数组分类为辅助任务，共享VGG-16前端，在ShanghaiTech和UCF_CC_50数据集上MAE分别降低5.8%、14.9%和10.5%。

通过CKLS--CIR变换对小型噪声CEV型扩散的弹性估计

Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions

针对小噪声CEV型扩散，提出基于CKLS-CIR变换的两步弹性估计器，证明其一致性与中心极限定理，并通过辅助CIR过程转移极限理论。

嵌入式多层回归与事后分层：在不完整辅助信息下的基于模型的推断

Embedded Multilevel Regression and Poststratification: Model-based Inference with Incomplete Auxiliary Information

针对MRP依赖辅助变量联合分布的限制，提出嵌入式MRP（EMRP）方法，在贝叶斯框架下生成合成总体并传播不确定性，模拟和实证表明其优于经典MRP及替代方法。

Recent progress in log-concave density estimation

In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one or more bandwidths. The purpose of this article is to describe some of the properties of the class of log-concave densities on $\mathbb{R}^d$ which make it so attractive from a statistical perspective, and to outline the latest methodological, theoretical and computational advances in the area.

Topological density estimation

We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We show that TDE has performance and runtime advantages over competing methods of kernel density estimation for highly multimodal probability density functions. We also show that TDE yields useful auxiliary information, that it can determine its own suitability for use, and we explain its performance.

迁移学习用于高维因子增强的稀疏线性模型

Transfer learning for high-dimensional Factor-augmented sparse linear model

本文研究高维因子增强稀疏线性模型的迁移学习，针对经济学和金融领域中强相关预测变量和潜在因子结构带来的估计挑战，提出方法以缓解高相关性和潜在因子影响，建立非渐近的ℓ1-和ℓ2-误差界，并提供假设检验框架和置信区间构造方法。

将条件密度估计转化为单一非参数回归任务

Transforming Conditional Density Estimation Into a Single Nonparametric Regression Task

本文提出将条件密度估计转化为单一非参数回归任务的方法，通过引入辅助样本，利用神经网络和决策树等高维回归方法，提升了估计效果。

Conditional Noise-Contrastive Estimation of Unnormalised Models

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random fields, and neural network models in unsupervised deep learning. In previous work, the estimation principle called noise-contrastive estimation (NCE) was introduced where unnormalised models are estimated by learning to distinguish between data and auxiliary noise. An open question is how to best choose the auxiliary noise distribution. We here propose a new…

Two-step estimation in linear regressions with adaptive learning

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares from an auxiliary model. The singular limiting distribution of the two-step estimator is normal and in general affected by the sampling uncertainty from the first step. However, this `generated-regressor' issue disappears for certain parameter combinations.

利用非参数方法有效估计非线性有限总体参数

Efficient Estimation of Nonlinear Finite Population Parameters Using Nonparametrics

目前，对基尼指数、低收入比例或其他衡量不平等程度的标准等非线性参数进行高精度估计尤为重要。在本文中，我们提出了一个一般类的估计这样的参数，考虑到单变量辅助信息假设是已知的人口中的每一个单位。通过非参数模型辅助的方法，我们构建了一个独特的调查权重系统，可以用来估计任何非线性参数与任何研究变量的调查，使用插件的原则。基于严格的功能方法和线性化原理，所提出的估计量的渐近方差推导，方差估计量是一致的温和的假设下。该理论是充分详细的惩罚B样条估计与实际实施的建议和指导方针，选择平滑参数。从法国劳动力调查中提取的数据证明了该方法的有效性。基尼系数和低收入比例的点和置信区间估计。理论和实证结果突出了我们的兴趣，在使用非参数方法与参数的辅助信息的存在下估计非线性参数。

Regularized Multi-Task Learning for Multi-Dimensional Log-Density Gradient Estimation

Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not necessarily lead to an accurate log-density gradient estimate. To cope with this problem, a method to directly estimate the log-density gradient without density estimation has been explored, and demonstrated to work much better than the two-step method. The objective of this paper is …

Bregman投影在调查抽样中的校准估计

Bregman projection for calibration estimation in Survey Sampling

提出基于Bregman散度的校准加权统一框架，揭示权重空间与乘子空间的对偶Bregman投影性质，并设计对比熵生成器实现泊松抽样下的设计最优性，扩展至非概率抽样的双稳健估计和高维辅助变量的正则化方法。

Generalized Linear Models for Longitudinal Data with Biased Sampling Designs: A Sequential Offsetted Regressions Approach

Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured response through an outcome-related, auxiliary variable. Such auxiliary variable- or outcome-dependent sampling improves observed response and possibly exposure variability over random sampling, {even though} the auxiliary variable is not of scientific interest. {For analysis,} we propose a generalized linear model based approach using a sequence of two offsetted r…

调查抽样中使用广义熵的去偏校准估计

Debiased calibration estimation using generalized entropy in survey sampling

本文提出以广义熵为目标函数、将设计权重置于约束中的新型校准加权框架，并确定最优广义熵选择以实现最小方差，从而改进调查抽样中的辅助信息利用效率。

A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements…