It is our purpose in this note to discuss three of the many approaches to seismic array processing from the theoretical point of view. The three are: 1) maximumlikelihood processing, 2) the minimum-variance, unbiased estimator (MVU) approach used by Levin, and 3) multichannel Wiener filtering. A feature common to these techniques is the formation of a single output waveform which serves as an e...

This paper uses Kalman filter theory to design a state estimator for noisy discrete time Takagi–Sugeno (T–S) fuzzy models. One local filter is designed for each local linear model using standard Kalman filter theory. Steady state solutions can be found for each of the local filters. Then a linear combination of the local filters is used to derive a global filter. The local filters are time-inva...

The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple examp...

Asymptotic distribution of the mean survival time based on the Kaplan-Meier curve with an extrapolated 'tail' is derived. A closed formula of the variance estimate is provided. Asymptotic properties of the estimator were studied in a simulation study, which showed that this estimator was unbiased with proper coverage probability and followed a normal distribution. An example is used to demonstr...

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Therefore, several standard theorems on properties of U-statistics apply. In particular, it has minimal variance among all unbiased estimators and is asymptotically normal...

In this paper we consider estimating heterogeneity variance with the DerSimonian-Laird (DSL) estimator as typically used in meta-analysis. In its general form the DSL estimator requires inverse population-averaged study-specific variances as weights, in which case the estimator is unbiased. It has become common practice, however, to use estimates of the study-specific variances instead of their...

Managers always consider the precise estimation of sediments in watersheds due to various conditions, such assoil and water resources management, construction, infrastructure and economical and social issues. In this condition,an optimized determination of sediment rating equation (typical method until now for sediment yield estimation) isessential to investigate sediment yield in rivers. In th...

‎In this paper‎, ‎we have dealt with the distribution theory of concomitants of order statistics arising from Farlie-Gumbel-Morgenstern bivariate Lomax distribution‎. ‎We have discussed the estimation of the parameters associated with the distribution of the variable Y of primary interest‎, ‎based on the ranked set sample defined by ordering the marginal observations...

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier and we propose an improved estimator of the population frontier. In addition, we provide the exact distribu...

A classical problem in many radar and sonar applications is the adaptive detection/esti-mation of a given signal in the presence of zero mean Gaussian noise. Reed, Mallett, and Brennan (RMB) derived and analyzed an adaptive detection scheme where the noise adaptation and non-trivial nature of their analysis resulted from the use of a noise sample covariance matrix (SCM). The case now considered...