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  2. Mean squared error - Wikipedia

    This property, undesirable in many applications, has led researchers to use alternatives such as the mean absolute error, or those based on the median. See also. Bias–variance tradeoff; Hodges' estimator; James–Stein estimator; Mean percentage error; Mean square quantization error; Mean square weighted deviation; Mean squared displacement

  3. Root-mean-square deviation - Wikipedia

    Formula. The RMSD of an estimator ^ with respect to an estimated parameter is defined as the square root of the mean square error: ⁡ (^) = ⁡ (^) = ⁡ ((^)). For an unbiased estimator, the RMSD is the square root of the variance, known as the standard deviation.

  4. Deviation (statistics) - Wikipedia

    In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set:

  5. Taylor's theorem - Wikipedia's_theorem

    Mean-value forms of the remainder — Let f : R → R be k + 1 times differentiable on the open interval with f (k) continuous on the closed interval between a and x. Then R k ( x ) = f ( k + 1 ) ( ξ L ) ( k + 1 ) !

  6. Median - Wikipedia

    In this context, there are several choices for a measure of variability: the range, the interquartile range, the mean absolute deviation, and the median absolute deviation. For practical purposes, different measures of location and dispersion are often compared on the basis of how well the corresponding population values can be estimated from a ...

  7. Sample size determination - Wikipedia

    Otherwise, the formula would be () = /, which yields = (). For example, if we are interested in estimating the proportion of the US population who supports a particular presidential candidate, and we want the width of 95% confidence interval to be at most 2 percentage points (0.02), then we would need a sample size of (1.96) 2 / (0.02 2 ) = 9604.

  8. Effect size - Wikipedia

    In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value.

  9. Chernoff bound - Wikipedia

    1) By performing the same analysis on the random variable -X, one can get the same bound in the other direction. Pr (X ≤ a) ≤ inf t ≥ 0 e t a ∏ i E ⁡ [e − t X i] {\displaystyle \Pr(X\leq a)\leq \inf _{t\geq 0}e^{ta}\prod _{i}\operatorname {E} \left[e^{-tX_{i}}\right]} Specific Chernoff bounds are attained by calculating the moment-generating function E ⁡ [e − t ⋅ X i ...

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