Two fundamental processes of modulation recognition are parameter extraction and feature selection. Parameter extraction determines unique characteristics of the signal such as frequency, phase, and amplitude. Parameters may also include statistical measures such as standard deviation, and nth-order moments and cumulants. This paper provides a brief review of two parameters, coherence and entro...

In many engineering applications, we have to combine probabilistic and interval errors. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only kno...

A wide range of econometric and statistical models are specified through moment conditions. Efficient estimation of such models essentially employs two distinct ideas: optimally combining estimation equations (e.g., the optimal estimating equations of Godambe (1976), the generalized method of moments of Hansen (1982) and the empirical likelihood of Qin and Lawless (1994)), and optimally combini...

We present a series of closed-form maximum entropy upper bounds for the differential entropy of a continuous univariate random variable and study the properties of that series. We then show how to use those generic bounds for upper bounding the differential entropy of Gaussian mixture models. This requires to calculate the raw moments and raw absolute moments of Gaussian mixtures in closed-form...

Diamagnetic susceptibilities of two series of organic compounds have been described by using a novel sub-structural approach. The method is based on the calculation of spectral moments of the bond adjacency matrix of molecular graphs. These spectral moments are expressed via algebraic expressions as linear combinations of simple fragments present in molecules. Contributions of each fragment to ...

Liver cancer leads to more number of human deaths nowadays. Patient survival chances can be increased by early detection of the tumour. Texture analysis based on moment features for CT liver scan images is proposed here. The texture feature is extracted by local binary pattern and statistical features are extracted by Legendre moments. This communication presents a comparative analysis between ...

Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N-body simulations – in a ΛCDM cosmology – are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combine...

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph...