Valid, prior-free, and situation-specific probabilistic inference is desirable for serious uncertain inference, especially in bio-medical statistics. This chapter∗ introduces such an inferential system, called the Inferential Model (IM) framework, proposed recently. IMs do not require a prior to be specified, yet they produce probabilistic inferential results that have desireable frequency prop...

 Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...

There are many statistical problems in which the parameter of interest is restricted to a subset of the parameter space. The constraint(s) may reflect prior knowledge about the value of the parameter, or, may be a device used to improve the statistical properties of the estimator. Estimation and inferential procedures for such models may be derived using the theorem of Kuhn-Tucker (KT). The the...

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...

Kernel density estimators are the basic tools for density estimation in non-parametric statistics.  The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. In this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...

In a recent paper James Bogen and James Woodward denounce a set of views on confirmation that they collectively brand ‘IRS’. The supporters of these views cast confirmation in terms of Inferential Relations between observational and theoretical Sentences. Against IRS accounts of confirmation, Bogen and Woodward unveil two main objections: (a) inferential relations are not necessary to model con...

State estimation is the foundation of any control and decision making in power networks. The first requirement for a secure network is a precise and safe state estimator in order to make decisions based on accurate knowledge of the network status. This paper introduces a new estimator which is able to detect bad data with few calculations without need for repetitions and estimation residual cal...

Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however, exhibiting some peculiar features that make them more ch...