A Statistical Model with Qualitative Input

TL;DR

This paper introduces a statistical estimation model that incorporates qualitative human intuition, analyzes its properties, and demonstrates its application in portfolio selection, highlighting the impact of variable correlation.

Contribution

It develops a new model integrating qualitative input into statistical estimation and explores its properties and practical application in finance.

Findings

Qualitative information can be as effective as quantitative data in the model.

Correlation between variables can reduce estimation accuracy.

The model shows promise for portfolio selection with financial data.

Abstract

A statistical estimation model with qualitative input provides a mechanism to fuse human intuition in the form of qualitative information into a statistical model. We investigate the statistical properties of this model and devise a numerical computation method for a model subclass with a uniform correlation structure. We show that, within this subclass, qualitative information can be as useful as quantitative information. We also show that the correlation between variables compromises the accuracy of the statistical estimate. However, the adverse effect from the correlation can be minimal, as is illustrated in an application to portfolio selection. The proposed model, when used in conjunction with approximation techniques, is shown to have potential for portfolio selection with financial data.