Identifying Nonlinear Covariate Effects in Semimartingale Regression Models

Abstract

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 stdy 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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA197323

Entities

People

  • Ian W. Mckeague
  • Klaus J. Utikal

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Classification
  • Convergence
  • Data Science
  • Differential Equations
  • Distribution Functions
  • Equations
  • Estimators
  • Goodness Of Fit Tests
  • Homogeneity
  • Information Science
  • Integrals
  • Probability
  • Statistics
  • Stochastic Processes
  • Survival
  • Universities
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms