Convergence Rate of Sieve Estimates

In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space and allow the size of the approximating space to grow as the sample size increases. This method is called the method of sieves. In the case of the maximum likelihood estimation, an MLE based on a sieve is called a sieve MLE. We found that the convergence rate of a sieve estimate is governed by (a) the local expected values, variances and $L_2$ entropy of the criterion differences and (b) the approximation error of the sieve. A robust nonparametric regression problem, a mixture problem and a nonparametric regression problem are discussed as illustrations of the theory. We also found that when the underlying space is too large, the estimate based on optimizing over the whole parameter space may not achieve the best possible rates of convergence, whereas the sieve estimate typically does not suffer from this difficulty.In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space and allow the size of the approximating space to grow as the sample size increases. This method is called the method of sieves. In the case of the maximum likelihood estimation, an MLE based on a sieve is called a sieve MLE. We found that the convergence rate of a sieve estimate is governed by (a) the local expected values, variances and $L_2$ entropy of the criterion differences and (b) the approximation error of the sieve. A robust nonparametric regression problem, a mixture problem and a nonparametric regression problem are discussed as illustrations of the theory. We also found that when the underlying space is too large, the estimate based on optimizing over the whole parameter space may not achieve the best possible rates of convergence, whereas the sieve estimate typically does not suffer from this difficulty.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）

笔记与分组

同方向的基础文献

相关领域论文

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel

Ameer Qaqish · Sudipto Banerjee · Didong Li首次提交 2026-10-07 · 修订 2026-10-13 · v2arXiv预印本

RBF 核高斯过程最大似然估计的精确渐近理论AI 解读

Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…

核、筛与局部多项式极大与准极大似然时间序列

被引：暂无数据

AI 解读阅读原文 ↗BibTeX ↓

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

Recursive-Head Geometry and Order-Free Efficient Inference in Finite-State Nested Markov Models

Haoyu Wei首次提交 2026-09-15 · 修订 2026-09-15 · v1arXiv预印本

有限状态嵌套 Markov 模型的递归头几何与无序有效推断AI 解读

Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither…

微观 · 因果推断核、筛与局部多项式极大与准极大似然

被引：暂无数据

AI 解读阅读原文 ↗BibTeX ↓

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

LOCAL POLYNOMIAL ESTIMATION OF TIME-VARYING PARAMETERS IN NONLINEAR MODELS

Dennis Kristensen · Young Jun Lee上线 2026-07-13Econometric Theory在线待刊

非线性模型时变参数的局部多项式估计AI 解读

We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time-series models, including discrete-valued ones. We show that the proposed estimators are asymptotically normally distributed under weak conditions. We also provide a precise characterization of the leading bias term due to smoothing. We demonstrate the usefulness of our general results by establishing primitive conditions for local…

宏观 · 时间序列结构变化与时变参数核、筛与局部多项式

被引 3 次 ↗OpenAlex · 核验 2026-09-30

AI 解读阅读原文 ↗BibTeX ↓

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions

Vanessa Rodriguez · Karla Diaz-Ordaz · Brieuc Lehmann · Mark J. van der Laan首次提交 2026-07-04 · 修订 2026-07-04 · v1arXiv预印本

目标函数的目标化高度自适应Lasso最小损失估计AI 解读

We propose a Targeted Highly Adaptive Lasso for estimation of non-pathwise differentiable functional parameters such as the dose-response curve (DRC) for continuous exposure. We assume the target function lies in the $k$-th order smoothness class used to define the $k$-th order Highly Adaptive Lasso (HAL), which can be well approximated by linear spans of $k$-th order spline basis functions. We construct a projection of the true target function onto a large finite…

微观 · 因果推断正则化与变量选择核、筛与局部多项式

关联记录被引 0 次 ↗OpenAlex · 核验 2026-10-12

AI 解读阅读原文 ↗BibTeX ↓

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

XMSE-Aware Adaptive Empirical Bayes Estimation

Minghao Chen · Jiale Zheng首次提交 2026-06-25 · 修订 2026-06-25 · v1arXiv预印本

XMSE 感知的自适应经验贝叶斯估计AI 解读

Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter. This paper turns that diagnostic into a design principle. We propose an XMSE-aware mixed estimator that interpolates between ML and EB shrinkage. Its fixed-weight…

贝叶斯 VAR 与局部投影核、筛与局部多项式

关联记录被引 0 次 ↗OpenAlex · 核验 2026-10-12

AI 解读阅读原文 ↗BibTeX ↓

共同方法：半参数与非参数、矩估计与似然、检验与推断、一般估计、核、筛与局部多项式、极大与准极大似然

Weak Moment Methods for Statistical Inference: with an Application to Robust Estimation

R. Labouriau首次提交 2026-04-26 · 修订 2026-06-24 · v2arXiv预印本

弱矩方法用于统计推断：兼论稳健估计应用AI 解读

A companion paper develops a generalised framework in which a probability law is represented by a tempered distribution $T\in\mathcal{S}'$ - on the same footing as a density or characteristic function - and information is extracted by pairing $T$ with a positive Schwartz kernel $\varphi$ that acts as a measurement instrument rather than as part of the law; the resulting weak moments of all orders exist unconditionally. The present paper turns this into a methodology for…

核、筛与局部多项式正则化与变量选择极大与准极大似然

关联记录被引 0 次 ↗OpenAlex · 核验 2026-10-12

AI 解读阅读原文 ↗BibTeX ↓