maximemetoden

Maximemetoden is a term used in some Swedish-language statistics and optimization literature to describe a class of parameter-estimation techniques in which the values of model parameters are chosen to maximize a specified objective function. While the exact objective can vary, the most common instantiation is maximizing a likelihood function based on observed data, i.e., maximum-likelihood estimation. Other variants may maximize a utility function, a posterior density (leading to maximum a posteriori estimation), or any scalar criterion that encodes goodness-of-fit or predictive performance.

Formally, given a model y = f(x; theta) and data D, maximemetoden seeks theta* = argmax_theta L(theta; D), where L is the chosen objective function. If L is differentiable, necessary conditions are obtained by setting the gradient to zero, and, in constrained problems, by using methods such as Lagrange multipliers or projection. Solutions may be obtainable analytically for simple models; in more complex cases, numerical methods are employed, including gradient ascent, Newton-Raphson, or expectation-maximization when latent variables are present.

Applications of maximemetoden span statistics, econometrics, machine learning, and engineering, wherever a model’s parameters are inferred by optimizing a criterion. The method is related to and often overlaps with least-squares approaches (as a special case of MLE under Gaussian errors) and with Bayesian methods when priors are incorporated.

Terminology varies by field; maximemetoden is not a standardized term in all disciplines. In many contexts it refers to maximum-criterion estimation, with the precise meaning depending on the chosen objective function and domain. See also maximum likelihood estimation, maximum a posteriori estimation, and optimization.