ParameterA parameter (), 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. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
Extremum estimatorIn statistics and econometrics, extremum estimators are a wide class of estimators for parametric models that are calculated through maximization (or minimization) of a certain objective function, which depends on the data. The general theory of extremum estimators was developed by . An estimator is called an extremum estimator, if there is an objective function such that where Θ is the parameter space. Sometimes a slightly weaker definition is given: where op(1) is the variable converging in probability to zero.
April 1974The following events occurred in April 1974: Born: Håkan Hellström, Swedish musician Died: Douglass Dumbrille, Canadian actor (b. 1889) Georges Pompidou, 100th Prime Minister of France and 19th President of France, Co-Prince of Andorra An enormous tornado outbreak strikes the central parts of the United States, killing around 319 and injuring about 5,484. Born: Died: Carrie, the debut novel by Stephen King, is published. Born: Died: A. Y. Jackson, Canadian painter and a founding member of the Group of Seven (b.
January 9681 – Twelfth Council of Toledo: King Erwig of the Visigoths initiates a council in which he implements diverse measures against the Jews in Spain. 1127 – Jin–Song Wars: Invading Jurchen soldiers from the Jin dynasty besiege and sack Bianjing (Kaifeng), the capital of the Song dynasty of China, and abduct Emperor Qinzong of Song and others, ending the Northern Song dynasty. 1349 – The Jewish population of Basel, believed by the residents to be the cause of the ongoing Black Death, is rounded up and incinerated.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Mean absolute percentage errorThe mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: where At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n.
Reduced chi-squared statisticIn statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) It is defined as chi-square per degree of freedom: where the chi-squared is a weighted sum of squared deviations: with inputs: variance , observations O, and calculated data C.
Fisher informationIn mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth).
January–March 2023 in scienceThis article lists a number of significant events in science that have occurred in the first quarter of 2023. 3 January – Researchers report molecular mechanisms that appear to underlie some of the reported health benefits of periods of intermittent fasting: changes to gene expression or rhythmicity of ~80% of genes in at least one tissue. 4 January – Metascientists introduce the 'CD index' intended to characterize "how papers and patents change networks of citations in science and technology" and report that it has declined, which they interpret as "slowing rates of disruption".
Bayes estimatorIn estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. Suppose an unknown parameter is known to have a prior distribution .
Observational errorObservational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken.
