Joint Distributions for Two Useful Classes of Statistics, With Applications to Classification and Hypothesis Testing

Abstract

In this paper, we analyze the statistics of two general classes of statistics. The first class is "M quadratic and linear forms of correlated Gaussian random variables". Examples include both cyclic and non-cyclic autocorrelation function (ACF) estimates of a correlated Gaussian process or the magnitude-squared of the output samples of a filtered Gaussian process. The second class consists of a subset of order statistics together with a remainder term. An example is the largest M - 1 bins of a discrete Fourier transform (DFT) or discrete wavelet transform (DWT), together with the sum of the remaining energies, forming an M-dimensional statistic. Both classes of statistics are useful in classification and detection of signals. In this paper, we solve for the joint probability density functions (PDFs) of both classes. Using the PDF projection method, these results can be used to transform the feature PDFs into the corresponding high-dimensional PDFs of the raw input data.

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Document Details

Document Type
Technical Report
Publication Date
Jan 10, 2002
Accession Number
ADA477219

Entities

People

  • Albert H. Nuttall
  • Paul Baggenstoss

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Classification
  • Computing-Related Activities
  • Data Science
  • Discrete Fourier Transforms
  • Gaussian Processes
  • Information Operations
  • Information Science
  • Interdisciplinary Science
  • Mathematics
  • Order Statistics
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistics
  • Undersea Warfare
  • Wavelet Transforms

Fields of Study

  • Engineering

Readers

  • Image Processing and Computer Vision.
  • Neural Network Machine Learning.
  • Statistical inference.