4 problems

Doss's localization conjecture. The quantity $E_{n,b}$ is asymptotically negligible for sufficiently large $n$ and $b$. This is intended to justify localization of the likelihood r…

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 neigh…

Let $2\log\lambda_n$ denote the likelihood ratio statistic for testing the value of a concave regression function, based on a null-constrained concave least-squares estimator. Doss…

In the equally spaced sequence formulation of concave regression, let $K_n$ be the cone of concave sequences in ${\mathbb R}^n$, let $\hat{\theta}$ be the least-squares estimator o…