Doss's Wilks phenomenon conjecture for concave regression

Assume the regression model holds with $Ee^{t\epsilon_{n,i}^2}<\infty$ for some $t>0$. Let $r_0$ be concave, satisfy $r_0(x_0)=y_0$, be twice continuously differentiable in a neighborhood of $x_0$, and satisfy $r_0”(x_0)<0$. Assume the stated design-density and local-uniform-design conditions hold, and let $\lambda_n(y_0)$ be the likelihood ratio statistic for testing $r_0(x_0)=y_0$. Doss's Wilks phenomenon conjecture. One has

$$2\log\lambda_n(y_0)\to_d\sigma^2\mathbb D,$$

where $\mathbb D$ is a universal random variable, independent of $r_0$ and of the distribution of $\epsilon_{n,i}$. This conjectures a universal, nuisance-parameter-free limit distribution, extending Wilks-type phenomena to concave regression; the source records analogous results in related shape-constrained models but does not establish this claim.