The detection of outliers is of critical importance in the assurance of data quality. Outliers may exist in observed data or in data derived from these observed data, such as estimates and forecasts. An outlier may indicate a problem with its data generation process or may simply be a true, but unusual, statement about the world. Without making any distributional assumptions, we proposes the use of loss functions to detect these outliers in panel data. Part I covers nonnegative data. We axiomatically derive an unsigned loss function. We then develop a signed loss function ito account for positive and negative outliers separately. In the case of nominal time we obtain an exact parametrization of the loss function. A time-invariant loss function permits the comparison of data at multiple times on the same basis. We provide several examples, including an example in which the outliers are classified by another variable. Part II covers data of mixed sign. Similar to Part I, we axiomatically develop unsigned and signed loss functions. We search for optimal values of the loss function parameter using graphs.

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