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In this paper, a general large deviation result for partial sums of independent and identically distributed random variables with super-heavy tailed distribution is established. Our main result extends in particular the results of Stoica (2008) and Nakata (2022). The symmetrization technique, one of Lévy's inequalities, and two preliminary results on slowly and regularly varying functions are paramount in the proof of our main result. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, we study the simple linear errors in variables (EV) model: , with i.i.d. errors . The consistency and asymptotic normality for the LS estimators and of the unknown parameters are obtained, which weaken some known conditions and improve some known results. Finally, the large deviation principle for and are given under the assumptions that possess normal distributions. [ABSTRACT FROM AUTHOR]

In the paper, the large deviation inequalities of the LS estimator for the nonlinear regression model with martingale differences errors are established. The assumptions for the errors are (conditional) exponential integrability which weaken the bounded condition in Hu (1993). As an application, we give the large deviation inequalities of LS estimator for the simple Michaelis–Menten model. [ABSTRACT FROM AUTHOR]