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...

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...

In this paper we derive some unbiased estimators of the population mean under simple inverse sampling with replacement, using the class of Hansen-Hurwitz and Horvitz-Thompson type estimators and the post-stratification approach. We also compare the efficiency of resulting estimators together with Murthy's estimator. We show that in despite of general belief, the strategy consisting of inverse s...

A method is presented for calculating the amount of information conveyed to a hearer by a speaker emitting a sentence generated by a probabilistic grammar known to both parties. The method applies the work of Grenander (1967) to the intermediate states of a top-down parser. This allows the uncertainty about structural ambiguity to be calculated at each point in a sentence. Subtracting these val...

The pattern theory of Grenander is a mathematical framework where the patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminative model is in the form of a classifier. It specifies the conditional pr...

Grenander's pattern theory ooers a uniied approach to characterizing variability in complex systems. Automatic target recognition systems for forward-looking infrared sensors must be robust to three kinds of variability: 1) Geometric variability-Target appearances vary with their orientations and positions; 2) Image variability-Target appearances vary with their thermodynamic state, and natural...