# Is this a typo in Stone's (1977) paper on asymptotic equivalence between AIC and LOOCV?

I am unsure about an expression in Stone's (1997) paper on asymptotic equivalence between AIC and LOOCV. Section 4., third line from the bottom of page 45 starts with $$L(\theta)-1(y_i|x_i,\theta)$$. The second part of this expression is puzzling to me.

What does $$1$$ stand for? An indicator function?
Or should it actually be $$l$$ rather than $$1$$, meaning the likelihood of a single observation $$l(y_i|x_i,\theta)$$?

References

This is definitely a typo. Note that $$\ell$$ stands for the log-likelihood, $$S=\{(x_i,y_i)\}$$ for the training data, $$S_{-i}$$ for the training data with the $$i$$-th entry removed (defined right before equation (3.3)), and $$L(\theta) = \sum_j\ell(y_j|x_j,\theta).$$
Finally, $$\hat\theta(S)$$ ("$$\hat\theta$$ for short") is defined as the maximizer of $$L(\theta)$$.
We are considering "$$\hat\theta(S_{-i})$$ ($$\hat\theta_{-i}$$ for short)". Per the definition of $$\hat\theta(S)$$, this is the maximizer of $$L(\theta)$$, but based on $$S_{-i}$$ instead of $$S$$, or
$$\sum_{j\neq i}\ell(y_j|x_j,\theta) = L(\theta)-\ell(y_i|x_i,\theta).$$
And Stone (1977) writes $$L(\theta)-1(y_i|x_i,\theta)$$ instead of the last expression. So the $$1$$ should be an $$\ell$$ here.
(Another argument for using $$\ell$$ instead of $$l$$. Some things do get better.)