Accession Number : ADA190857

Title :   Inference for a Nonlinear Semimartingale Regression Model.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : McKeague, Ian W ; Utikal, Klaus J

PDF Url : ADA190857

Report Date : Nov 1987

Pagination or Media Count : 25

Abstract : This document considers a semimartingale regression model where Y, Z are observable covariate processes alpha is a (deterministic) function of both, time and the covariate process Z, and M is a square integrable martingale. Under the assumption that i.i.d. copies of X, Y, Z are observed continuously over a finite time interval, inference for the function alpha (t, z) is investigated. An estimator A (caret) for the time integrated alpha (t, z) and a kernel estimator of alpha (t, z) itself for introduced. For X a counting process, A (caret) reduces to the Nelson-Aalen estimator when Z is not present in the model. Various forms of consistency are proved, rates of convergence and asymptotic distributions of the estimators are derived. Asymptotic confidence bands for the time integrated alpha (t,z) and a Kolmogorov-Smirnov-type test of equality of alpha at different levels of the covariate are given.

Descriptors :   *MATHEMATICAL MODELS, *REGRESSION ANALYSIS, *STATISTICAL INFERENCE, *NONLINEAR SYSTEMS, ASYMPTOTIC SERIES, CONVERGENCE, COUNTING METHODS, ESTIMATES, KERNEL FUNCTIONS, RATES, TIME INTERVALS, COVARIANCE, STATISTICAL TESTS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE