DeepAI AI Chat
Log In Sign Up

Goodness-of-Fit Test for Self-Exciting Processes

06/16/2020
by   Song Wei, et al.
0

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications, notably self- and mutual- exciting point processes. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit test framework to evaluate their performance. In this paper, we provide goodness-of-fit tests for generative models by leveraging a new connection of this problem with the classical statistical theory of mismatched maximum-likelihood estimator (MLE). We present a non-parametric self-normalizing test statistic for the goodness-of-fit test based on Generalized Score (GS) statistics. We further establish asymptotic properties for MLE of the Quasi-model (Quasi-MLE), asymptotic χ^2 null distribution and power function of GS statistic. Numerical experiments validate the asymptotic null distribution as well as the consistency of our proposed GS test.

READ FULL TEXT
06/17/2018

On APF Test for Poisson Process with Shift and Scale Parameters

We propose the goodness of fit test for inhomogeneous Poisson processes ...
07/20/2020

Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling

Goodness-of-fit (GoF) testing is ubiquitous in statistics, with direct t...
02/08/2022

Testing Linearity for Network Autoregressive Models

A quasi-score linearity test for continuous and count network autoregres...
10/13/2020

Generalized Rescaled Pólya urn and its statistical applications

We introduce the Generalized Rescaled Pólya (GRP) urn. In particular, th...
09/04/2017

Learning Implicit Generative Models Using Differentiable Graph Tests

Recently, there has been a growing interest in the problem of learning r...
07/22/2022

Modelling Equity Transaction Networks as Bursty Processes

Trade executions for major stocks come in bursts of activity, which can ...
10/28/2022

Evaluation of Categorical Generative Models – Bridging the Gap Between Real and Synthetic Data

The machine learning community has mainly relied on real data to benchma...