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In this paper, we obtain the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression models under some mild conditions. And we also show that those conditions are necessary in some sense.

We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function.

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For x ∈ I, let [A1(x), A2(x), …] be the continued fraction expansions over the field of Laurent series, write Ln(x) ≔ max { deg A1(x), deg A2(x), …, deg An(x)}, which is called the largest degree of partial quotients. In this paper, we give an iterated logarithm type theorem for Ln(x), and by which, we get that for P-almost all x ∈ I, [Formula: see text]. Also the Hausdorff dimensions of the related exceptional sets are determined.