The conditional distance autocovariance function

2021 ◽  
Author(s):  
Qiang Zhang ◽  
Wenliang Pan ◽  
Chengwei Li ◽  
Xueqin Wang
Keyword(s):  
Autocovariance Function

scholarly journals Decoding 2-D Maps by Autocovariance Function

2016 ◽  
pp. 39-53
Author(s):  
Maria Chiara Pietrogrande ◽  
Nicola Marchetti ◽  
Francesco Dondi
Keyword(s):  
Autocovariance Function

CHARACTERIZATION OF NUCLEAR IMAGES BASED ON ANALYSIS OF FRACTIONAL SUMMATION SYSTEMS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 157-169 ◽  
Author(s):  
HAI-SHAN WU ◽  
ANDREW J. EINSTEIN ◽  
LIANE DELIGDISCH ◽  
TAMARA KALIR ◽  
JOAN GIL
Keyword(s):  
White Noise ◽  
Frequency Domain ◽  
Discrete System ◽  
Fractional Integral ◽  
Continuous System ◽  
Time Range ◽  
System Function ◽  
Autocovariance Function ◽  
Frequency Domain Methods

While frequency-based methods for the characterization of fractals are popular and effective in many applications, they have limitations when applied to irregularly shaped images, such as nuclear images. The irregularity renders texture characterization by frequency domain methods, based upon Fourier transform, problematic. To address this situation, this paper presents an algorithm based upon the signal analysis in the spatial domain. An autocovariance function can be estimated regardless of the shape and size of regions where the image is defined. As in the continuous fractional Brownian motion (FBM) that results from inputting white noise into a specific fractional integral system, a discrete FBM can be related to white noise by a specific fractional summation system (FSS) that is linear, causal and shift-invariant. Although the method of direct sampling is not valid for converting a continuous fractional integral to a discrete fractional summation, discrete fractional summations similar to the sampled system functions can be obtained through an iterative process. While the continuous system function of a fractional integral is linear in the frequency domain when plotted in log-log scales, unfortunately, it is not true for the comparable discrete system function. The discrete system function is actually approximately linear in the log-log scales over a very limited range. The slope of the straight line that approximates the function curve in the mean-square-error (MSE) sense in a specific time range provides a description of the autocovariance function that reveals the statistical relations among the local textures. Applications to characterization of ovary nuclear images in groups of normal, atypical and cancer cases are studied and presented.

SUPERPOSITIONED STATIONARY COUNT TIME SERIES

2019 ◽  
pp. 1-19
Author(s):  
Yisu Jia ◽  
Robert Lund ◽  
James Livsey
Keyword(s):  
Time Series ◽  
Negative Binomial ◽  
Stationary Sequence ◽  
Time Series Models ◽  
Count Time Series ◽  
Marginal Distributions ◽  
Autocovariance Function ◽  
Basic Properties ◽  
Model Class ◽  
Discrete Uniform

Abstract This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

scholarly journals Robust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processes

2010 ◽  
Vol 32 (2) ◽  
pp. 135-156 ◽  
Author(s):  
Céline Lévy-Leduc ◽  
Hélène Boistard ◽  
Eric Moulines ◽  
Murad S. Taqqu ◽  
Valderio A. Reisen
Keyword(s):  
Long Range ◽  
Robust Estimation ◽  
Autocovariance Function ◽  
Dependent Processes

A weak convergence theorem for the empirical characteristic function

1975 ◽  
Vol 12 (3) ◽  
pp. 515-523 ◽  
Author(s):  
John T. Kent
Keyword(s):  
Weak Convergence ◽  
Characteristic Function ◽  
Gaussian Process ◽  
Convergence Theorem ◽  
Stationary Gaussian Process ◽  
Empirical Characteristic Function ◽  
Autocovariance Function ◽  
Weak Convergence Theorem

The purpose of this paper is to show that the empirical characteristic function, when suitably normalised, converges weakly to a stationary Gaussian process whose autocovariance function is the theoretical characteristic function.

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