OPTION 1: Delete the items with missing data. The remaining set has no missing data. This approach may produce bias. The result may not be representative of the intended forecast subject mater.

OPTION 2: Use imputation. Imputation means use the most probable values to substitute the missing data. in order to properly impute missing values, it is necessary to verify the pattern of the missing data. See attached files.

Generally, there are 2 approaches:

(i) Monotone Missing data. If the pattern of the missing data is monotonal, use parametric regression that assumes multivariate normality or non-parametric that uses propensity score. An article dealing with this score is attached.

(ii) Arbitrary Missing Data. If the pattern of the missing data is arbitrary, i.e. no structure or predictable pattern, apply the Markov Chain Monte Carlo (MCMC) with assumed multivariate normality.

In both (i) and (ii), you might want to run a randomness tests to verify whether the missing data is a random occurrence. After all the data has been filled (imputed), you are ready for TE calculation.

STOCHASTIC FRONTIER: If starting with the stochastic frontier model:

(1)   Yi = f(x; B) exp(vi)exp(ui)

x = input vector;

Y = output by producer i;

f(x; B) = production function where B = technology;

exp(vi) = stochastic component of production function; and

exp(ui) = inefficiency captured by noise level ui.

The technical efficiency may be given by:

(2)   TE = Yi / [f(x; B)exp(v)]

A unity means that the system is 100% efficient. The noise ui = log / TE. The production function f(x) may be in the form of Cobb-Douglas or trans-log.

REFERENCES: See attached articles.

Thank you  sir Paul for your valuable information. very helpful---

Probably you May use a fuzzy approach by estimating the missing data (for instance by means of the standard deviation of the other ones)

Two stage methodology could be useful in this perspective, where use fuzzy in first stage and DEA in second.