# Cram\'er Type Moderate Deviations for Random Fields

## TL;DR

This paper investigates Cramér type moderate deviations for partial sums of random fields, utilizing the conjugate method, with applications to linear random fields and nonparametric regression errors.

## Contribution

It introduces new results on moderate deviations for random fields, extending classical theory to complex dependence structures and practical regression models.

## Key findings

- Established Cramér type moderate deviation results for linear random fields.
- Extended applicability to nonparametric regression with random field errors.
- Demonstrated the effectiveness of the conjugate method in this context.

## Abstract

We study the Cram\'er type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric regression with random field errors.