Ordinary least squares ( OLS ) is often used for estimation since it provides the BLUE or " best linear unbiased estimator " ( where " best " means most efficient, unbiased estimator ) given the Gauss-Markov assumptions.

The Gauss-Markov theorem shows that the OLS estimator is the best ( minimum variance ), unbiased estimator assuming the model is linear, the expected value of the error term is zero, errors are homoskedastic and not autocorrelated, and there is no perfect multicollinearity.

Error terms are assumed to be spherical otherwise the OLS estimator is inefficient.

When x and the other unmeasured, causal variables collapsed into the term are correlated, however, the OLS estimator is generally biased and inconsistent for β.

When the covariates are exogenous, the small-sample properties of the OLS estimator can be derived in a straightforward manner by calculating moments of the estimator conditional on X.

The violation causes OLS estimator to be biased and inconsistent.

Given a positive estimator, a positive covariance will lead OLS estimator to overestimate the true value of an estimator.

The OLS estimator is consistent when the regressors are exogenous and there is no perfect multicollinearity, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated.

Under the additional assumption that the errors be normally distributed, OLS is the maximum likelihood estimator.

As in the standard case, the maximum likelihood estimator ( MLE ) estimator of the covariance matrix differs from the ordinary least squares ( OLS ) estimator.

OLS estimator: for a model with a constant, k variables and p lags.

This implies that the regression coefficient in an Ordinary Least Squares ( OLS ) regression is biased, however if the correlation is not contemporaneous, then it may still be consistent.

Autocorrelation violates the ordinary least squares ( OLS ) assumption that the error terms are uncorrelated.

While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated ( and the t-scores overestimated ) when the autocorrelations of the errors at low lags are positive.

The sample data matrix must have full rank or OLS cannot be estimated.

The commercial timesharing services such as CompuServe, On-Line Systems ( OLS ), and Rapidata maintained sophisticated inhouse systems programming groups so that they could modify the operating system as needed for their own businesses without being dependent on DEC or others.

( The error term does not get included in the expectation values as it is assumed that it satisfies the usual OLS conditions, i. e., E ( U < sub > i </ sub >)

One such method is the usual OLS method, which is called the Linear probability model, this is only in case of an independent dummy variable regression.

There are several basic types of discrepancy functions, including maximum likelihood ( ML ), generalized least squares ( GLS ), and ordinary least squares ( OLS ), which are considered the " classical " discrepancy functions.

This method differs from the Ordinary Least Squares ( OLS ) statistical technique that bases comparisons relative to an average producer.

The other two are the Linux Symposium ( commonly known as OLS ) and Linux Kongress.

Oracle has a product named Oracle Label Security ( OLS ) that implements mandatory access controls-typically by adding a ' label ' column to each table in an Oracle database.

OLS is being deployed at the US Army INSCOM as the foundation of an " all-source " intelligence database spanning the JWICS and SIPRNet networks.

This is the ( ordinary ) least squares ( OLS ) approach.

Following an internal outcry, the Sadiq al-Mahdi government in March 1989 agreed with the United Nations and donor nations ( including the US ) on a plan called Operation Lifeline Sudan ( OLS ), under which some 100, 000 tons of food was moved into both government and SPLA-held areas of the Sudan, and widespread starvation was averted.

Phase II of OLS to cover 1990 was approved by both the government and the SPLA Sudan faced a 2-year drought and food shortage across the entire country.

In 1965 Eisenstadt convinced Bernhard to use a statistical method called ordinary least squares ( OLS ) regression analysis to replace Bernhard's visual method of fitting cash flow to a price chart.

In 1992 the local shooting club ( Schutterij St. Joseph ) won the OLS.

The Sargan test statistic can be calculated as ( the number of observations multiplied by the coefficient of determination ) from the OLS regression of the residuals onto the set of exogenous variables.

The estimator is an unbiased estimator of if and only if.

Often, people refer to a " biased estimate " or an " unbiased estimate ," but they really are talking about an " estimate from a biased estimator ," or an " estimate from an unbiased estimator.

In fact, even if all estimates have astronomical absolute values for their errors, if the expected value of the error is zero, the estimator is unbiased.

The ideal situation, of course, is to have an unbiased estimator with low variance, and also try to limit the number of samples where the error is extreme ( that is, have few outliers ).

In particular, for an unbiased estimator, the variance equals the MSE.

An estimator is unbiased if its expected value is the true value of the parameter ; It is consistent if it converges to the true value as sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size.

where is the unique symmetric unbiased estimator of the third cumulant and is the symmetric unbiased estimator of the second cumulant.

While the first one may be seen as the variance of the sample considered as a population, the second one is the unbiased estimator of the population variance, meaning that its expected value E is equal to the true variance of the sampled random variable ; the use of the term n − 1 is called Bessel's correction.

Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically efficient as the maximum likelihood estimator ; however, the maximum likelihood estimate is difficult to compute, leaving the truncated mean as a useful alternative.

) More commonly, however, the expected value ( mean or average ) of the sampled values is chosen ; this is a Bayes estimator that takes advantage of the additional data about the entire distribution that is available from Bayesian sampling, whereas a maximization algorithm such as expectation maximization ( EM ) is capable of only returning a single point from the distribution.

The sample covariance matrix ( SCM ) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R < sup > p × p </ sup >; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator.

Intuitively one wants to choose h as small as the data allow, however there is always a trade-off between the bias of the estimator and its variance ; more on the choice of bandwidth later.