# A Weighted Model Confidence Set: Applications to Local and Mixture Model Confidence Sets

## TL;DR

This paper introduces a weighted model confidence set designed for situations where models are misspecified but certain data regions are informative, with applications demonstrated in local and mixture models through simulations.

## Contribution

It proposes a novel weighted confidence set approach that accounts for model misspecification and emphasizes informative data regions, extending traditional confidence set methods.

## Key findings

- Effective in identifying true models under misspecification
- Applicable to local and mixture models with promising results
- Validated through two simulation studies

## Abstract

This article provides a weighted model confidence set, whenever underling model has been misspecified and some part of support of random variable $X$ conveys some important information about underling true model. Application of such weighted model confidence set for local and mixture model confidence sets have been given. Two simulation studies have been conducted to show practical application of our findings.