Inference for a Nonlinear Semimartingale Regression Model.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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.
- Statistics and Probability