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Definition. One common method of construction of a multivariate t-distribution, for the case of dimensions, is based on the observation that if and are independent and distributed as (,) and (i.e. multivariate normal and chi-squared distributions) respectively, the matrix is a p × p matrix, and is a constant vector then the random variable = / / + has the density
The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
Wald test. In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate. [1] [2] Intuitively, the larger this weighted distance, the ...
The Cochran–Armitage test for trend, [1] [2] named for William Cochran and Peter Armitage, is used in categorical data analysis when the aim is to assess for the presence of an association between a variable with two categories and an ordinal variable with k categories. It modifies the Pearson chi-squared test to incorporate a suspected ...
Definition. Suppose that we have a statistical model of some data. Let k be the number of estimated parameters in the model. Let ^ be the maximized value of the likelihood function for the model. Then the AIC value of the model is the following. = (^)
Computations or tables of the Wilks' distribution for higher dimensions are not readily available and one usually resorts to approximations. One approximation is attributed to M. S. Bartlett and works for large m allows Wilks' lambda to be approximated with a chi-squared distribution
X ∼ N C χ k ( 0 ) {\displaystyle X\sim NC\chi _ {k} (0)} In other words, the chi distribution is a special case of the non-central chi distribution (i.e., with a non-centrality parameter of zero). A noncentral chi distribution with 2 degrees of freedom is equivalent to a Rice distribution with. σ = 1 {\displaystyle \sigma =1}
Hellinger distance. In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f -divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by ...