Statistical Inference Based on Data Tilting

基于数据倾斜的统计推断

• 批准号: 0403443
• 负责人: Liang Peng
• 金额: $ 8.56万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0403443&HistoricalAwards=false
• 关键词: Statistical; Inference; Based; Data; Tilting

The investigator studies three subjects: extreme valuetheory, ARCH/GARCH models, and nonparametric regression with censoreddata. The particular issues examined in this proposal include:1) constructing confidence intervals for high quantilesin risk management; 2) constructing confidence intervalsfor the difference of two means with heavy tails; 3)constructing confidence intervals for parameters in ARCH/GARCHmodels; 4) constructing a confidence interval for the maximalmoment exponent of a GARCH (1,1) sequence; 5) forecasting the1-step ahead conditional Value-at-Risk based on GARCH models;6) applying the data tilting method to obtain confidenceintervals for the tail index of a double autoregressive model;and 7) applying the data tilting method to obtain confidenceintervals for a conditional survival function with censored data.The proposed activity described above involvesnovel applications of data tilting methods. The researchapproach is a combination of theoretical asymptotic analysis,Monte Carlo simulation and real data analysis.The problems studied in this project arise from real applications in various fields includingmeteorology, hydrology, insurance, andfinance. Examples are: in the design of electricaldistribution systems and buildings, the extremes of wind pressure loading must be accounted for;insurers who underwrite the financial risk associated with natural risks like floods, storms and earthquakes must have good estimates of the size and impact of extreme events inorder to set their premiums at a profitable level.This project studies the following issues: modeling extremeevents; predicting Value-at-Risk in riskmanagement; estimating frontier functions for comparing the performance of different firms; estimating parametersof volatility models in financial time series; and estimating theconditional life time in assessing the influence of risk factorson survival. Progress in this project can enhancethe interaction among several areas in statistical science, includingextreme value theory, nonparametric smoothing, time series analysis,and survival analysis. The new methods to be developedcan be applied to financial time series, sea level prediction,internet traffic data, medical data, to name a few. Thetheoretical asymptotic results to be developed are expected to havebroader applications as well.

研究者研究三个主题：极值理论，GARCH/GARCH模型，和删失数据的非参数回归。本文研究的具体问题包括：1）风险管理中高分位数的置信区间的构造; 2）重尾均值差的置信区间的构造; 3）GARCH/GARCH模型参数的置信区间的构造; 4）GARCH（1，1）序列最大矩指数的置信区间的构造; 5）基于GARCH模型预测一步前条件风险值（Value-at-Risk）：6）应用数据倾斜方法获得双自回归模型尾部指标的置信区间;以及7）应用数据倾斜方法获得删失数据条件生存函数的置信区间。上述活动涉及数据倾斜方法的新应用。本课题的研究方法是理论渐近分析、蒙特卡罗模拟和真实的数据分析相结合的方法，所研究的问题来自气象、水文、保险、金融等领域的真实的应用。 示例如下：在配电系统和建筑物的设计中，必须考虑到极端的风压负荷，承保洪水、风暴和地震等自然风险的保险公司必须对极端事件的规模和影响有很好的估计，以便将其保费定在盈利水平。本文的主要研究内容包括：金融时间序列中波动率模型的参数估计;风险因素对生存影响的一致性寿命估计。 该项目的进展可以增强统计科学中几个领域之间的相互作用，包括极值理论，非参数平滑，时间序列分析和生存分析。 新的方法可以应用于金融时间序列，海平面预测，互联网流量数据，医疗数据，仅举几例。所得到的理论渐近结果也可望有更广泛的应用。