Statistical Inference Based on Data Tilting

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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.