Parameter vs. Estimator — What's the Difference?

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean.

A numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation

To calculate approximately (the amount, extent, magnitude, position, or value of something).

A limit or boundary which defines the scope of a particular process or activity

To form an opinion about; evaluate

A constant in an equation that varies in other equations of the same general form, especially such a constant in the equation of a curve or surface that can be varied to represent a family of curves or surfaces.

A tentative evaluation or rough calculation, as of worth, quantity, or size

One of a set of independent variables that express the coordinates of a point.

A statement of the approximate cost of work to be done, such as a building project or car repairs.

One of a set of measurable factors, such as temperature and pressure, that define a system and determine its behavior and are varied in an experiment.

A judgment based on one's impressions; an opinion

Usage Problem A factor that restricts what is possible or what results

A person who estimates, especially one who estimates costs

A factor that determines a range of variations; a boundary

(mathematics) A function of a random sample of a population used to estimate some parameter of the whole population

(Statistics) A quantity, such as a mean, that is calculated from data and describes a population.

One who estimates or values; a valuer.

Usage Problem A distinguishing characteristic or feature.

An expert at calculation (or at operating calculating machines)

A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.

(sciences) A variable that describes some system (material, object, event, etc.) or some aspect thereof.

(statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.

(machine learning) A variable of a model that is trained by a machine learning algorithm.

(programming) An input variable of a function definition, that gets an actual value (argument) at execution time.

An actual value given to such a formal parameter.

A characteristic or feature that distinguishes something from others.

(geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.

(crystallography) The ratio of the three crystallographic axes which determines the position of any plane.

(crystallography) The fundamental axial ratio for a given species.

A constant number which is part of a theory, function, or calculation, whose value is not determined by the form of the theory or equation itself, and may in some cases be arbitrary assigned.

A term applied to some characteristic magnitude whose value, invariable as long as one and the same function, curve, surface, etc., is considered, serves to distinguish that function, curve, surface, etc., from others of the same kind or family.

Any constant number which is required to calculate values of observed phenomena according to a theory, but the value of which must be determined by experiment, and cannot be calculated from the fundamental assumptions of the theory. In general, a theory which has a large number of parameters, though it may accurately predict experimental results, is considered as having less explanatory power and as being less esthetically pleasing than a theory with fewer parameters.

The ratio of the three crystallographic axes which determines the position of any plane; also, the fundamental axial ratio for a given species.

The limits, guidelines, or assumptions from within which an activity is carried out; as, new arrivals need to learn the parameters of the research in our department.

A variable used in a calculation within a computer program which must be assigned a value before the calculation can be performed; as, let's plug in the parameters and see what the result is.

A characteristic or element, especially one used as a criterion for evaluation or judgment; as, a useful parameter for determining efficiency.

A constant in the equation of a curve that can be varied to yield a family of similar curves

Any factor that defines a system and determines (or limits) its performance

A quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data