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The weighted mean in this case is: ¯ = ¯ (=), (where the order of the matrix–vector product is not commutative), in terms of the covariance of the weighted mean: ¯ = (=), For example, consider the weighted mean of the point [1 0] with high variance in the second component and [0 1] with high variance in the first component.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Kernel average smoother example. The idea of the kernel average smoother is the following. For each data point X 0, choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than to X 0 (the closer to X 0 points get higher weights).
Python: the KernelReg class for mixed data types in the statsmodels.nonparametric sub-package (includes other kernel density related classes), the package kernel_regression as an extension of scikit-learn (inefficient memory-wise, useful only for small datasets) R: the function npreg of the np package can perform kernel regression. [7] [8]
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
An exponential moving average (EMA), also known as an exponentially weighted moving average (EWMA), [5] is a first-order infinite impulse response filter that applies weighting factors which decrease exponentially. The weighting for each older datum decreases exponentially, never reaching zero. This formulation is according to Hunter (1986). [6]
It is a measure used to evaluate the performance of regression or forecasting models. It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [3]
The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures, the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal. However, it ...