{
  "id": "enwiki-001259440311",
  "slug": "mean-signed-deviation",
  "title": "Mean signed deviation",
  "qid": "",
  "lead": "In statistics, the mean signed difference (MSD), also known as mean signed deviation, mean signed error, or mean bias error is a sample statistic that summarizes how well a set of estimates \\hat{\\theta}_i match the quantities \\theta_i that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available. Then \\theta_i would be the i-th out-of-sample value of the dependent variable, and \\hat{\\theta}_i would be its predicted value. The mean signed deviation is the average value of \\hat{\\theta}_i-\\theta_i.",
  "body": "In statistics, the mean signed difference (MSD), also known as mean signed deviation, mean signed error, or mean bias error is a sample statistic that summarizes how well a set of estimates \\hat{\\theta}_i match the quantities \\theta_i that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available. Then \\theta_i would be the i-th out-of-sample value of the dependent variable, and \\hat{\\theta}_i would be its predicted value. The mean signed deviation is the average value of \\hat{\\theta}_i-\\theta_i. ==Definition== The mean signed difference is derived from a set of n pairs, ( \\hat{\\theta}_i,\\theta_i) , where \\hat{\\theta}_i is an estimate of the parameter \\theta in a case where it is known that \\theta=\\theta_i . In many applications, all the quantities \\theta_i will share a common value. When applied to forecasting in a time series analysis context, a forecasting procedure might be evaluated using the mean signed difference, with \\hat{\\theta}_i being the predicted value of a series at a given lead time and \\theta_i being the value of the series eventually observed for that time-point. The mean signed difference is defined to be \\operatorname{MSD}(\\hat{\\theta}) = \\frac{1}{n}\\sum^{n}_{i=1} \\hat{\\theta_{i}} - \\theta_{i} . The mean signed difference is often useful when the estimations \\hat{\\theta_i} are biased from the true values \\theta_i in a certain direction. If the estimator that produces the \\hat{\\theta_i} values is unbiased, then \\operatorname{MSD}(\\hat{\\theta_i})=0 . However, if the estimations \\hat{\\theta_i} are produced by a biased estimator, then the mean signed difference is a useful tool to understand the direction of the estimator's bias. ==See also== Bias of an estimator Deviation (statistics) Mean absolute difference Mean absolute error ==References==",
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    "title": "Mean signed deviation",
    "author": [
      {
        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
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    "container-title": "encyclopegia.org",
    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/mean-signed-deviation",
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          15
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