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For correlated random variables the sample variance needs to be computed according to the Markov chain central limit theorem.. Independent and identically distributed random variables with random sample size
Definition and basic properties. The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
This t-statistic can be interpreted as "the number of standard errors away from the regression line." Regressions. In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent ...
where represents the standard deviation of the function , represents the standard deviation of , represents the standard deviation of , and so forth.. It is important to note that this formula is based on the linear characteristics of the gradient of and therefore it is a good estimation for the standard deviation of as long as ,,, … are small enough.
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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).. Effectively, this overcomes the 'infinite error' issue. Its formula is:
Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result, the formula can be used as a measure of the bias in the forecasts. A disadvantage of this measure is that it is undefined whenever a single actual value is zero. See also