Spectral Analysis: Spectral analysis is concerned with estimation of the spectrum of a stationary random process or a stationary time series from the observed realization(s) of the process (or series). Methods and concepts of spectral analysis play an important role in time series analysis and signal processing . Browse Other...
View Full DescriptionSpectrum: See Fourier spectrum and power spectrum . Browse Other Glossary Entries
View Full DescriptionSpatial Field: A spatial field is a function of spatial variables , or in 3D cases. A spatial field is named a "scalar field" if the function takes on scalar values. For example, the concentration of a toxic substance in the soil at points with coordinates is a scalar field....
View Full DescriptionSmoothing: Smoothing is a class of time series processing which is intended to reduce noise and to preserve the signal itself. The origin of this term is related to the visual appearance of the time series - it looks smoother after this sort of processing than does the original time...
View Full DescriptionSampling Frame: Sampling frame (synonyms: "sample frame", "survey frame") is the actual set of units from which a sample has been drawn: in the case of a simple random sample, all units from the sampling frame have an equal chance to be drawn and to occur in the sample. In...
View Full DescriptionSmoother (Smoothing Filter): Smoothers, or smoothing filters, are algorithms for time-series processing that reduce abrupt changes in the time-series and make it look smoother. Smoothers constitute a broad subclass of filters. Like all filters, smoothers may be subdivided into linear and nonlinear. Linear filters reduce the power of higher frequencies...
View Full DescriptionSmoother (Example): A simple example of a smoother is the moving average procedure. It is based on averaging elements closest in time to the current time. Mathematically this can be expressed by the following simple formula: where is the input of the smoother, the original time series; is the output...
View Full DescriptionSocial Network Analytics: Network analytics applied to connections among humans. Recently it has come also to encompass the analysis of web sites and internet services like Facebook. Browse Other Glossary Entries
View Full DescriptionSingle Linkage Clustering: The single linkage clustering method (or the nearest neighbor method) is a method of calculating distance between clusters in hierarchical cluster analysis . The linkage function specifying the distance between two clusters is computed as the minimal object-to-object distance , where objects belong to the first cluster,...
View Full DescriptionSimple Linear Regression: The simple linear regression is aimed at finding the "best-fit" values of two parameters - A and B in the following regression equation: where Yi, Xi, and Ei are the values of the dependent variable, of the independent variable, and of the random error, respectively. Parameter A...
View Full DescriptionSignal: The signal is the component of the observed data (e.g. of a time series ) that carries useful information. The complementary (opposite) concept is noise . In a narrower sense (e.g. in signal processing ) signals are functions of time, as opposed to fields (functions of spatial coordinates) or...
View Full DescriptionSignal Processing: Signal processing is a branch of applied statistics concerned with analysis of functions of time that take on scalar or vector values. The functions are normally mixtures of a signal and a noise . A broad range of topics are considered in signal processing, including estimation of the...
View Full DescriptionShift Invariance (of Measures): Shift invariance is a property of descriptive statistics . If a statistic is shift-invariant, it possesses the following property for any data set : or, in equivalent form In other words, if a statistic is shift-invariant, then addition of an arbitrary value , positive or negative,...
View Full DescriptionStatistical Glossary Seemingly Unrelated Regressions (SUR): Seemingly unrelated regressions (SUR) is a class of multivariate regression ( multiple regression ) models, normally belonging to the sub-class of linear regression models. A distinctive feature of SUR models is that they consist of several unrelated systems of equations "Unrelated" here means that...
View Full DescriptionSeasonal Decomposition: The seasonal decomposition is a method used in time series analysis to represent a time series as a sum (or, sometimes, a product) of three components - the linear trend, the periodic (seasonal) component, and random residuals. The seasonal decomposition is useful in analysis of time series affected...
View Full DescriptionSeasonal Adjustment: The seasonal adjustment is used in time series analysis to remove a periodic component with the known period from the observed time series. This adjustment is normally performed through the seasonal decomposition of the time series followed by subtraction of the seasonal component from the observed data. The...
View Full DescriptionStatistical Glossary Scale Invariance (of Measures): Scale invariance is a property of descriptive statistics . If a statistic is scale-invariant, it has the following property for any sample and any non-negative value : (1) or, in mathematically equivalent form In other words, if a statistic is scale-invariant, then multiplication of...
View Full DescriptionSample Survey: In a sample survey , a sample of units drawn from the population of interest is analyzed. A related concept is the census survey . The main advantage of the sample survey (as compared to the census survey ) is that its implementation is technically simpler - because...
View Full DescriptionStatistical Significance: Outcomes to an experiment or repeated events are statistically significant if they differ from what chance variation might produce. For example - suppose n people are given a medication. If their response to the medication lies outside the range of how samples of size n might respond when...
View Full DescriptionSampling: Sampling is a process of drawing a sample from a population . Sampling may be performed from both real and hypothetical populations. Examples of sampling from a real population are opinion polls (when a finite number of individuals is chosen from a much bigger group, say, a population of...
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