Inference for a Nonlinear Semimartingale Regression Model.

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1987
Accession Number
ADA190857

Entities

People

  • Ian W. Mckeague
  • Klaus J. Utikal

Organizations

  • Florida State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Consistency
  • Convergence
  • Data Science
  • Decomposition
  • Diffusion
  • Estimators
  • Gaussian Processes
  • Inequalities
  • Information Science
  • Intervals
  • Probability
  • Security
  • Statistical Inference
  • Time Intervals
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.

Technology Areas

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