We consider the problem of estimating the modal value of a decreasing density on the positive real line. This has application in several interesting phenomena arising, for example, in renewal theory, and in biased and distance samplings. We use a penalized likelihood ratio-based approach for...

We consider the estimation of a monotone function at its end-point, where the least square estimate is inconsistent. The least square criterion is penalized to achieve consistency. The limit distribution for the residual sum of squares is derived, to construct confidence intervals.

The supremum difference between the cumulative sum diagram, and its greatest convex minorant (GCM), in case of non-parametric isotonic regression is considered. When the regression function is strictly increasing, and the design points are unequally spaced, but approximate a positive density in...