# Model Mismatch Trade-offs in LMMSE Estimation

arXiv: https://arxiv.org/abs/2105.11964 · HTML: https://mlsanity.com/paper/2105.11964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 3 of 3)

- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Robust Prediction when Features are Missing](https://mlsanity.com/paper/1912.07226/) (2019)
- [Generalization Error for Linear Regression under Distributed Learning](https://mlsanity.com/paper/2004.14637/) (2020)

## Built on by (most cited first, 1 of 1)

- [Estimation under Model Misspecification with Fake Features](https://mlsanity.com/paper/2203.03398/) (2022)

## Abstract (arXiv)

We consider a linear minimum mean squared error (LMMSE) estimation framework with model mismatch where the assumed model order is smaller than that of the underlying linear system which generates the data used in the estimation process. By modelling the regressors of the underlying system as random variables, we analyze the average behaviour of the mean squared error (MSE). Our results quantify how the MSE depends on the interplay between the number of samples and the number of parameters in the underlying system and in the assumed model. In particular, if the number of samples is not sufficiently large, neither increasing the number of samples nor the assumed model complexity is sufficient to guarantee a performance improvement.