lokimäärien

Lokimäärien (local quantities) are terms used to describe values that characterize a specific location within a domain, derived from information available in a surrounding neighborhood. They arise in many fields—mathematics, statistics, physics, engineering—to capture spatially varying properties.

In formal terms, a lokimäärä is a quantity attached to a point x in a space X that is determined predominantly by nearby data rather than global structure. Locality is often implemented via a neighborhood N(x) or a scale parameter that defines which nearby points influence the value. This concept underpins local estimators, densities, and field values.

Examples include local density estimates in spatial statistics, where the density at a position is inferred from nearby observations; local energy or mass density in physics; and local averages, gradients, or texture measures in image processing.

Applications and considerations: The choice of neighborhood or scale affects the lokimäärien, influencing bias and variance. In heterogeneous or boundary regions, locality may be restricted or biased; methods often incorporate kernels or weighting schemes to modulate influence with distance or direction.

See also: Local function, kernel density estimation, local indicators of spatial association, locality in mathematics.