CovarianceIn probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative.
Nonparametric regressionNonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. That is, no parametric form is assumed for the relationship between predictors and dependent variable. Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates.
Cross-covariance matrixIn probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable. Each element has either a finite number of observed empirical values or a finite or infinite number of potential values. The potential values are specified by a theoretical joint probability distribution.
Local regressionLocal regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced ˈloʊɛs. They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model.
Course-of-values recursionIn computability theory, course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion, the value of f(n) is computed from the sequence . The fact that such definitions can be converted into definitions using a simpler form of recursion is often used to prove that functions defined by course-of-values recursion are primitive recursive.
CorecursionIn computer science, corecursion is a type of operation that is to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data.
Estimation of covariance matricesIn statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix.
Mean absolute percentage errorThe mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: where At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n.
Mean squared errorIn statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.
Cross-covarianceIn probability and statistics, given two stochastic processes and , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation for the expectation operator, if the processes have the mean functions and , then the cross-covariance is given by Cross-covariance is related to the more commonly used cross-correlation of the processes in question.
