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In programming language theory, lazy evaluation, or call-by-need, [1] is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (by the use of sharing). [2] [3] The benefits of lazy evaluation include:
Vector autoregressions are flexible statistical models that typically include many free parameters. Given the limited length of standard macroeconomic datasets relative to the vast number of parameters available, Bayesian methods have become an increasingly popular way of dealing with the problem of over-parameterization. As the ratio of ...
In general, with a normally-distributed sample mean, Ẋ, and with a known value for the standard deviation, σ, a 100(1-α)% confidence interval for the true μ is formed by taking Ẋ ± e, with e = z 1-α/2 (σ/n 1/2), where z 1-α/2 is the 100(1-α/2)% cumulative value of the standard normal curve, and n is the number of data values in that ...
[3] [4] [5] The primary aim of estimation methods is to report an effect size (a point estimate) along with its confidence interval, the latter of which is related to the precision of the estimate. [6] The confidence interval summarizes a range of likely values of the underlying population effect.
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
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. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...
One can normalize input scores by assuming that the sum is zero (subtract the average: where =), and then the softmax takes the hyperplane of points that sum to zero, =, to the open simplex of positive values that sum to 1 =, analogously to how the exponent takes 0 to 1, = and is positive.
Let the unknown parameter of interest be , and assume we have a statistic such that the expected value of m is μ: [] =, i.e. m is an unbiased estimator for μ. Suppose we calculate another statistic t {\displaystyle t} such that E [ t ] = τ {\displaystyle \mathbb {E} \left[t\right]=\tau } is a known value.