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In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a ...
Estimation theory. Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate ...
Time series. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily ...
Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. [10] Statistical techniques are widely used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image ...
Maximum likelihood estimation (MLE) is a standard statistical tool for finding parameter values (e.g. the unmixing matrix ) that provide the best fit of some data (e.g., the extracted signals ) to a given a model (e.g., the assumed joint probability density function (pdf) of source signals).
In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter. The result is named in honor of Harald Cramér and C. R. Rao, [1][2][3] but has also been derived independently by Maurice Fréchet, [4] Georges Darmois, [5] and by Alexander Aitken and Harold ...
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. [1][2][3] Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as ...
Moving-average model. In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [1][2] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.