What issue arises from a low sample size in RMSE calculations?

In RMSE (Root Mean Square Error) calculations, the primary concern with a low sample size relates to the reliability and validity of the error estimate. A low sample size does not inherently prevent RMSE from being calculated; it can still be computed mathematically. However, the insights gained from it may be misleading.

The most significant issue that arises from a small sample size is that it increases the potential for error in representing the overall population or dataset. With fewer data points, any anomalies or outliers have a proportionally larger impact on the RMSE, which can skew the results. Consequently, this leads to a higher likelihood that the calculated RMSE does not reflect the true error of the model when applied to a larger set of data.

In practice, a smaller sample might obscure the model's true predictive capability, as it may not adequately capture the variability and complexity of the underlying data, resulting in unreliable performance metrics. Therefore, while RMSE can be computed with a low sample size, it is the potential for error and misrepresentation that is of primary concern, highlighting the importance of using a sufficiently large and representative sample in any modeling efforts.