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Estimation (or estimating) is the process of finding an estimate or
approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...
, which is a value that is usable for some purpose even if input data may be
incomplete Incomplete may refer to: * Unfinished creative work * An incomplete formal system, see Completeness (logic) * Gödel's incompleteness theorems, a specification of logic * Incomplete (Bad Religion song), "Incomplete" (Bad Religion song), 1994 * Inco ...
, uncertain, or
unstable In dynamical systems instability means that some of the outputs or internal state (controls), states increase with time, without bounds. Not all systems that are not Stability theory, stable are unstable; systems can also be marginal stability ...
. The value is nonetheless usable because it is derived from the best information available.C. Lon Enloe, Elizabeth Garnett, Jonathan Miles, ''Physical Science: What the Technology Professional Needs to Know'' (2000), p. 47. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter".Raymond A. Kent, "Estimation", ''Data Construction and Data Analysis for Survey Research'' (2001), p. 157. The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeds the actual result and an underestimate if the estimate falls short of the actual result. The confidence in an estimate is quantified as a confidence interval, the likelihood that the estimate is in a certain range. Human estimators systematically suffer from
overconfidence The overconfidence effect is a well-established bias in which a person's subjective ''confidence'' in their judgments is reliably greater than the objective ''accuracy'' of those judgments, especially when confidence is relatively high. Overconfide ...
, believing that their estimates are more accurate than they actually are.


How estimation is done

Estimation is often done by sampling, which is counting a small number from a selected subset, and projecting that number onto a larger population. An example of estimation would be determining how many candies of a given size are in a glass jar. Because the distribution of candies inside the jar may vary, the observer can count the number of candies visible through the glass, consider the size of the jar, and presume that a similar distribution can be found in the parts that can not be seen, thereby making an estimate of the total number of candies that could be in the jar if that presumption were true. Estimates can similarly be generated by projecting results from polls or surveys onto the entire population. In making an estimate, the goal is often most useful to generate a range of possible outcomes that is precise enough to be useful but not so precise that it is likely to be inaccurate. For example, in trying to guess the number of candies in the jar, if fifty were visible, and the total volume of the jar seemed to be about twenty times as large as the volume containing the visible candies, then one might simply project that there were a thousand candies in the jar. Such a projection, intended to pick the single value that is believed to be closest to the actual value, is called a
point estimate In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown popu ...
. However, a point estimation is likely to be incorrect, because the sample size—in this case, the number of candies that are visible—is too small a number to be sure that it does not contain anomalies that differ from the population as a whole. A corresponding concept is an
interval estimate In statistics, interval estimation is the use of sample data to estimate an '' interval'' of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. The most prevalent forms of interval es ...
, which captures a much larger range of possibilities, but is too broad to be useful. For example, if one were asked to estimate the percentage of people who like candy, it would clearly be correct that the number falls between zero and one hundred percent. Such an estimate would provide no guidance, however, to somebody who is trying to determine how many candies to buy for a party to be attended by a hundred people.


Uses of estimation

In mathematics,
approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...
describes the process of finding estimates in the form of upper or lower bounds for a quantity that cannot readily be evaluated precisely, and
approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...
deals with finding simpler functions that are close to some complicated function and that can provide useful estimates. In statistics, an
estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on Sample (statistics), observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguish ...
is the formal name for the rule by which an estimate is calculated from data, and
estimation theory Estimation theory is a branch of statistics that deals with estimating the values of Statistical parameter, parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such ...
deals with finding estimators with good properties. This process is used in
signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...
, for approximating an unobserved signal on the basis of an observed signal containing noise. For estimation of yet-to-be observed quantities,
forecasting Forecasting is the process of making predictions based on past and present data. Later these can be compared with what actually happens. For example, a company might Estimation, estimate their revenue in the next year, then compare it against the ...
and
prediction A prediction (Latin ''præ-'', "before," and ''dictum'', "something said") or forecast is a statement about a future event or about future data. Predictions are often, but not always, based upon experience or knowledge of forecasters. There ...
are applied. A
Fermi problem A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme scientific calculatio ...
, in physics, is one concerning estimation in problems that typically involve making justified guesses about quantities that seem impossible to compute given limited available information. Estimation is important in business and economics because too many variables exist to figure out how large-scale activities will develop. Estimation in project planning can be particularly significant, because plans for the distribution of labor and purchases of raw materials must be made, despite the inability to know every possible problem that may come up. A certain amount of resources will be available for carrying out a particular project, making it important to obtain or generate a
cost estimate A cost estimate is the approximation of the cost of a program, project, or operation. The cost estimate is the product of the cost estimating process. The cost estimate has a single total value and may have identifiable component values. A proble ...
as one of the vital elements of entering into the project. The U.S. Government Accountability Office defines a cost estimate as, "the summation of individual cost elements, using established methods and valid data, to estimate the future costs of a program, based on what is known today", and reports that "realistic cost estimating was imperative when making wise decisions in acquiring new systems".''GAO Cost Estimating and Assessment Guide, Best Practices for Developing and Managing Capital Program Costs, GAO-09-3SP'', United States Government Accountabity Office, March 2009, Preface p. i. Furthermore, project plans must neither underestimate the needs of the project, which can result in delays while unmet needs are fulfilled, nor must they greatly overestimate the needs of the project, or else the unneeded resources may go to waste. An informal estimate when little information is available is called a
guesstimate ''Guesstimate'' is an informal English portmanteau of ''guess'' and '' estimate'', first used by American statisticians in 1934 or 1935.estimated sign The estimated sign or estimated symbol, , (officially, the ℮-mark or the final EC verification mark in EU law,) can be found on most prepackaged products in the European Union (EU). Its use indicates that the prepackage fulfils EU Directive 76 ...
'', ℮, is used to designate that package contents are close to the nominal contents.


See also

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Abundance estimation Abundance estimation comprises all statistical methods for estimating the number of individuals in a population. In ecology, this may be anything from estimating the number of daisies in a field to estimating the number of blue whale The ...
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Ansatz In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural ansatzes or, from German, ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be ...
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Ballpark estimate ''Guesstimate'' is an informal English portmanteau of ''guess'' and ''estimate'', first used by American statisticians in 1934 or 1935.Back-of-the-envelope calculation A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope. It is more than a guess but less than an accurate calculation or mathematical proof. The defining characteristic o ...
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Conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...
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Cost estimate A cost estimate is the approximation of the cost of a program, project, or operation. The cost estimate is the product of the cost estimating process. The cost estimate has a single total value and may have identifiable component values. A proble ...
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Estimation statistics Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. It complement ...
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Estimation theory Estimation theory is a branch of statistics that deals with estimating the values of Statistical parameter, parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such ...
*
Fermi problem A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme scientific calculatio ...
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German tank problem German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...
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State observer In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the state space (controls), internal state of a given real system, from measurements of the Input/output, input and output of th ...
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Kalman filter In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...
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Intuition Intuition is the ability to acquire knowledge without recourse to conscious reasoning or needing an explanation. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledg ...
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Mark and recapture Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. A portion of the population is captured, marked, and released. Later, another portion will be captu ...
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Moving horizon estimation Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables or parameters. Unlike determi ...
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Sales quote A request for quotation (RfQ) is a business process in which a company or public entity requests a quote from a supplier for the purchase of specific products or services. RfQ generally means the same thing as Call for bids (CfB) and Invitati ...
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Upper and lower bounds In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of . Dually, a lower bound or minorant of is defined to be an element of that is less th ...


References


External links


Estimation chapter from "Applied Software Project Management" (PDF)
{{Authority control Estimation theory