An M-estimator is

An M-estimator is

• A. A measure of dispersion.
• B. A robust measure of location, such as the median.
• C. A trimmed mean used to remove all outliers.
• D. A test statistic for parametric tests.

Answer: (B)

M-estimators are a robust way to estimate a location parameter by solving an estimating equation that comes from minimizing a sum of a chosen function of the deviations. This approach downweights or limits the influence of outliers, making the estimate more resistant to extreme values than the simple mean. For location, you can pick different rho functions; using the absolute value loss (rho(u) = |u|) leads to the median as the minimizer, which is a classic example of a robust location estimator. More generally, M-estimators include other robust options like Huber’s estimator, which behave like the mean for small residuals but resist outliers for large residuals. So an M-estimator is a robust measure of location, such as the median, rather than a measure of dispersion, a trimmed mean, or a test statistic for parametric tests.

M-estimators are a robust way to estimate a location parameter by solving an estimating equation that comes from minimizing a sum of a chosen function of the deviations. This approach downweights or limits the influence of outliers, making the estimate more resistant to extreme values than the simple mean.

For location, you can pick different rho functions; using the absolute value loss (rho(u) = |u|) leads to the median as the minimizer, which is a classic example of a robust location estimator. More generally, M-estimators include other robust options like Huber’s estimator, which behave like the mean for small residuals but resist outliers for large residuals.

So an M-estimator is a robust measure of location, such as the median, rather than a measure of dispersion, a trimmed mean, or a test statistic for parametric tests.