The Effect of Weight Trimming on Nonlinear Survey Estimates

The Effect of Weight Trimming on Nonlinear Survey Estimates was written by Frank J. Potter in 1993. It was part of the proceedings of the American Statistical Association Section on Survey Research Methods.

The author examines strategies/algorithms for weight trimming. "The ultimate goal of weight trimming is to reduce the sampling variance more than enough to compensate for the possible increase in bias..."

First strategies considered:

1. MSE of regression coefficients
   • requires a regression model of interest

   • regress with untrimmed weights, making note of the estimated coefficient of interest (β)

   • for every considered trimming level...

     • re-regress, making note of the estimated coefficient of interest (β_t) and Taylor-linearized variance

     • estimate the MSE of the trimmed coefficient as: MSE(β_t) = Var(β_t) + (β_t - β)²

     • estimate the squared relative bias as Rel Bias(β_t) = [(β_t - β)/β]²

   • with these estimates produced for all considered trimming levels:
     • assign ranks to each level by both MSE and squared relative bias
     • average the ranks
     • pick the level with the lowest average rank
2. MSE of means
   • essentially the same as above, but:
     • requires multiple metrics of interest

     • for each metric, estimate MSE as: MSE(Ȳ_t) = Var(Ȳ_t) + (Ȳ_t - Ȳ)²

     • assign ranks to each level by every metric
     • average the ranks
     • pick the level with the lowest average rank
3. A Taylor linearization variate
4. The procedure used for the National Assessment of Educational Progress
5. A weight distribution

   • A Beta distribution is estimated from weight statistics, with a cumulative distribution function as F_W(w).

   • A trimming level w_op is set for the weights based on a criterion; for example, if the criterion is 0.01, then the trimming level satisfies 1 - F_W(w_op) = 0.01.

The author finds that #1 is the best strategy with respect to both variance and bias. #2 and #3 result in very similar outcomes.

CategoryRicottone