Identifying Nonlinear Covariate Effects in Semimartingale Regression Models

摘要

Let X sub t be a semimartingale which is either continuous or of counting process type and which satisfies the stochastic differential equation dX sub t = Y sub t alpha(t, Z sub t) dt + dM sub t, where Y and Z are predictable covariate processes, M is a martingale and alpha is an unknown, nonrandom function. The authors study inference for alpha by introducing an estimator and deriving a functional central limit theorem for it. The asymptotic distribution turns out to be given by a Gaussian random field that admits a representation as a stochastic integral with respect to a multiparameter Wiener process. This result is used to develop a test for independence of X from the covariate Z, a test for time-homogeneity o alpha, and a goodness-of-fit test for the proportional hazards model alpha (t,z) = alpha sub 1 (t) alpha sub 2 (z) used in survival analysis. (KR)