Noise heteroscedastic

Profiles in the Presence of Homoscedastic or Heteroscedastic Noise, Anal. Chem. 66, 1994, 43-51. 

A similar effect is observed when non-interacting factors are not controlled. However, uncontrolled non-interacting factors usually produce homoscedastic noise (see Figure 3.6) uncontrolled interacting factors often produce heteroscedastic noise (see Figure 3.7), as they do in the present example. 

Keller, H.R., Massart, D.L., Liang, Y.Z., and Kvalheim, O.M., Evolving factor analysis in the presence of heteroscedastic noise, Anal. Chim. Acta, 263, 29-36, 1992. 

Heteroscedastic noise. This type of noise is dependent on signal intensity, often proportional to intensity. The noise may still be represented by a normal distribution, but the standard deviation of that distribution is proportional to intensity. A form of heteroscedastic noise often appears to arise if the data are transformed prior to processing, a common method being a logarithmic transform used in many types of spectroscopy such as UV/vis or IR spectroscopy, from transmittance to absorbance. The true noise distribution is imposed upon the raw data, but the transformed information distorts this. 

C.R. Mittermayr, E. Rosenberg and M. Grasserbauer, Detection and Estimation of Heteroscedastic Noise by Means of the Wavelet Transform, Analytical Communnication, 34 (1997), 73-78. 

Woodward, A. M., Alsberg, B. K. Kell, D. B. (1997) The effect of heteroscedastic noise on the modelling of frequency domain data. Appl. Spectroscopy, submitted... 

Heteroscedastic noise. This type of noise is dependent on signal intensity, often proportional to intensity. The noise may still be represented by a normal distribution, but the standard deviation of that distribution is proportional to intensity. 

Smoothing Methods Applied to Dealing with Heteroscedastic Noise in GC/MS. 

In order to apply RBL or GRAFA successfully some attention has to be paid to the quality of the data. Like any other multivariate technique, the results obtained by RBL and GRAFA are affected by non-linearity of the data and heteroscedast-icity of the noise. By both phenomena the rank of the data matrix is higher than the number of species present in the sample. This has been demonstrated on the PCA results obtained for an anthracene standard solution eluted and detected by three different brands of diode array detectors [37]. In all three cases significant second eigenvalues were obtained and structure is seen in the second principal component. 

Examples of noise. From the top noise free, homoscedastic, heteroscedastic... 

It is also the case that calibration data obtained as Rj"/Rsis" function of Qa /Qsis intrinsically heteroscedastic in cases where the concentrations are so low that statistical variations in ion counts (shot noise. Section 7.1.1) dominate the experimental variance. This can be demonstrated for a model (Schoeller 1976) that assumes that a fixed total amount of material is analyzed for each Qa"/Qsis" ratio, and that the ion currents for the two species (analyte and SIS) are integrated for the same length of time then it is straightforward to show (not done here) that the variance of the measurement of Ra VRsis" ill increase linearly with Ra"/Rsis"f°r values <0.1, and as (Rj VRsis 0 Ra VRsis > 10- F°r 0.1 < Rj VRsis < 10> increases as [(Ra /Rsis 0 + (Ra /Rsis 0 ]/QsiS In practice other experimental uncertainties will contribute to the total variance, but it is clear that data of this type can never be exactly homoscedastic. 

Heteroscedastic backgrounds can confound signals in a way that simple wavelet thresholding routines become ineffective at removing their influences. The changing variance of this noise allows the noise to move from one... 

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