The problem we are seeking to solve is the continual estimation of a set of parameters whose values change over time. Updating is achieved by combining a set of observations or measurements z(t) which contain information about the signal of interest x(t). The role of the estimator is to provide an estimate x̂(t+ ) at some time t+ . If > 0 we have a prediction filter, if < 0 a smoothing filter an...

We consider the problem of estimating the variance of a population using judgment post-stratification. By conditioning on the observed vector of ordered instratum sample sizes, we develop a conditionally unbiased nonparametric estimator that outperforms the sample variance except when the rankings are very poor. This estimator also outperforms the standard unbiased nonparametric variance estima...

Problem Statement: The four-parameter exponentiated generalized Lomax distribution has been introduced. The uniformly minimum variance unbiased and maximum likelihood estimation methods are the way to estimate the parameters of the distribution. In this study we explore and compare the performance of the uniformly minimum variance unbiased and maximum likelihood estimators of the reliability fu...

The Garman–Klass unbiased estimator of the variance per unit time of a zero–drift Brownian Motion (B), based on the usual financial data that reports for time windows of equal length the open (OPEN), minimum (MIN), maximum (MAX) and close (CLOSE) values, is quadratic in the statistic S1 = (CLOSE − OPEN, OPEN − MIN,MAX − OPEN). This estimator, with efficiency 7.4 with respect to the classical es...

Carrier phase ambiguity resolution is the key to high-precision global navigation satellite system (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. The so-called ‘fixed’ baseline estimator is known to be superior to its ‘float’ counterpart in the sense that its probability of being close to the unknown but true bas...

In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...

A joint estimator is presented for the two parameters that define the long-range dependence phenomenon in the simplest case. The estimator is based on the coefficients of a discrete wavelet decomposition, improving a recently proposed wavelet-based estimator of the scaling parameter [4], as well as extending it to include the associated power parameter. An important feature is its conceptual an...