Semi-parametric and Nonparametric Inference

半参数和非参数推理

• 批准号: RGPIN-2022-04799
• 负责人: Huang, MeiLing
• 金额: $ 1.31万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758623
• 关键词: Semi; parametric; Nonparametric; Inference

Objectives of the Proposed Research Program: The objective of my research is to develop novel inference methodology in two areas: 1) Inference methods for heavy-tailed distributions and networks. 2) Weighted and nonparametric inference for quantile regression; Train high quality personnel (HQP) to carry out research. 1. Inference for Heavy-Tailed Distributions and Networks Extreme events occur in financial markets, natural disasters, disease control and industrial risk. It is important to find suitable mathematical models for analyzing of extreme events where heavy-tailed distributions are usually applied. There are theoretical difficulties in the inference of heavy-tailed distributions. The proposed program explores three innovative inference objectives to overcome difficulties: Objective (1)(Prop) . Inference for Distributions and Quantiles: Explore new methods to reduce bias and errors for estimation of high quantiles and distributions. Compare new methods with existing methods theoretically and computationally. Objective (2)(Prop). Cluster and Approximation for Heavy Tailed Distributions: Heavy tailed data is often complicated, such that a single distribution may not fit data well. Explore new cluster, Hermite series, hyperexponential approximation methods for estimating heavy tailed distributions. Objective (3)(Prop). Inference for stochastic Models and Random Networks: Explore innovative inference methods on extreme renewal process and random network related to heavy tailed distributions theoretically and computationally. 2. Weighted and Nonparametric Inference for Quantile Regression Estimation on the tail of a conditional distribution is a challenging objective. This work focuses on estimating the conditional quantiles (Quantile Regression). I will study two novel objectives as follows: Objective (4)(Prop). Weighted Methods for Quantile Regression: Explore the optimal weights that minimize the estimation errors. Utilize several criteria for measurement of the errors. Objective (5)(prop). Direct Nonparametric Methods for Quantile Regression: Develop nonparametric quantile regression with more effective algorithms. Study theoretical efficiency, consistency, rate of convergence, and robustness. Assessment of the Proposed Objectives (1) to (5) 1) The theoretical approach includes probability theory, statistical theory, stochastic processes, integral equations, combinatorics, groups, and approximation. 2) The computational approach includes Monte Carlo simulations, bootstrapping, to confirm the theoretic results. 3) Applications on real-word examples, find best model fitting data with reasonable conclusions. Expected Significance: The program provides a new alternative approach for Statistical inference. The results are expected to overcome theoretical and computational difficulties in this field. The program trains HQPs to bring new ideas and skills for building suitable Mathematical models to solve real-world problems.

拟议的研究计划的目标：我的研究的目的是在两个领域开发新的推理方法：1）用于重尾分布和网络的推理方法。 2）分位数回归的加权和非参数推断；培训高质量人员（HQP）进行研究。 1。重型分布和网络的推断极端事件发生在金融市场，自然灾害，疾病控制和工业风险中。重要的是要找到合适的数学模型，以分析通常应用重尾分布的极端事件。重型分布的推断存在理论上的困难。拟议的计划探讨了克服困难的三个创新推理目标：目标（1）（prop）。分布和分位数的推断：探索新方法，以减少估计高分子和分布的偏差和错误。将新方法与现有方法在理论上和计算上进行比较。 目标（2）（Prop）。重型尾部分布的群集和近似值：重型尾部数据通常很复杂，因此单个分布可能不符合数据。探索新的簇，赫米特系列，过度近似近似方法，用于估计重型尾部分布。 目标（3）（Prop）。随机模型和随机网络的推断：探索与极端更新过程和随机网络有关的创新推理方法，与重型尾部分布有关，理论上和计算上。 2。对条件分布尾部的分位数回归估计的加权和非参数推断是一个具有挑战性的目标。这项工作着重于估计条件分位数（分位数回归）。我将研究两个新的目标：目标（4）（Prop）。分位数回归的加权方法：探索最小化估计误差的最佳权重。利用几个标准来测量错误。 目标（5）（Prop）。直接的非参数回归方法：使用更有效的算法开发非参数分位数回归。研究理论效率，一致性，收敛速度和鲁棒性。评估提出的目标（1）至（5）1）理论方法包括概率理论，统计理论，随机过程，积分方程，组合，组，组和近似值。 2）计算方法包括蒙特卡洛模拟，自举，以确认理论结果。 3）在现实词的示例中的应用，找到具有合理结论的最佳模型拟合数据。 预期意义：该计划为统计推断提供了一种新的替代方法。预计结果将克服该领域的理论和计算困难。该计划训练HQP，为建立合适的数学模型来解决现实世界中的问题带来新的想法和技能。