Search results
Results from the WOW.Com Content Network
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
where the function is the tilted absolute value function. The intuition is the same as for the population quantile. ... Matlab function quantreg [27] gretl has the ...
The converse, though, does not necessarily hold: for example, taking f as =, where V is a Vitali set, it is clear that f is not measurable, but its absolute value is, being a constant function. The positive part and negative part of a function are used to define the Lebesgue integral for a real-valued function.
The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by [1] This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where . The variable a often refers to the residuals ...
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the L 1 norm of such values.
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it.
Sign function. In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero. In mathematical notation the sign function is often represented as or .
Smooth maximum. In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function meaning a parametric family of functions such that for every α, the function is smooth, and the family converges to the maximum function as . The concept of smooth minimum is ...