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The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals.
An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism. [ 2 ] Anomalies are instances or collections of data that occur very rarely in the data set and whose features differ significantly from most of the data.
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
Random noise is often a large component of the noise in data. [3] Random noise in a signal is measured as the signal-to-noise ratio. Random noise contains almost equal amounts of a wide range of frequencies, and is also called white noise (as colors of light combine to make white). Random noise is an unavoidable problem.
The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n samples of a data set, centred on the mean of a normal distribution.By doing this, any data point from the n samples that lies outside this probability band can be considered an outlier, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size ...
The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented underlying model structure. [3]: 45 Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data.
Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters. The mathematical limits for noise removal are set by information theory .
Assumption: signal and (additive) noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation Requirement: the filter must be physically realizable/ causal (this requirement can be dropped, resulting in a non-causal solution)