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e. In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an n th degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E ( y | x ).
Trend-stationary process. In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. [1] The trend does not have to be linear.
Quadratic growth. In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit ", as the argument or sequence position goes to infinity – in big Theta notation ...
Curve fitting. Fitting of a noisy curve by an asymmetrical peak model, with an iterative process ( Gauss–Newton algorithm with variable damping factor α). Curve fitting[ 1][ 2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [ 3] possibly subject to constraints. [ 4][ 5 ...
Local regression or local polynomial regression, [ 1] also known as moving regression, [ 2] is a generalization of the moving average and polynomial regression. [ 3] Its most common methods, initially developed for scatterplot smoothing, are LOESS ( locally estimated scatterplot smoothing) and LOWESS ( locally weighted scatterplot smoothing ...
Autoregressive model. 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 ...
In multilevel modeling, an overall change function (e.g. linear, quadratic, cubic etc.) is fitted to the whole sample and, just as in multilevel modeling for clustered data, the slope and intercept may be allowed to vary. For example, in a study looking at income growth with age, individuals might be assumed to show linear improvement over time.
Its quadratic variation is the process, written as , defined as. where ranges over partitions of the interval and the norm of the partition is the mesh. This limit, if it exists, is defined using convergence in probability. Note that a process may be of finite quadratic variation in the sense of the definition given here and its paths be ...