Definition of Maximum Score Estimator: A maximum score estimator is a nonparametric estimator of certain coefficients of a binary choice model. Avoids assumptions about the distribution of errors that would be made by a probit or logit model in the same circumstances.

In the econometric model: the dependent variable y_i is either zero or one; the regressors X_i are multiplied by a parameter vector b. y_i often represents which of two choices was selected by a respondent. b is estimated to maximize an objective function that is given by an expression:

max_b sum_{i=1 to N} [(y_i-.5)sign(X_ib)]

where i indexes observations, of which there are N, and the function sign() has value one if its argument is greater than or equal to zero, and has value zero otherwise.

b chosen this way has the property that it maximizes the correct prediction of y_i given the information in X. Notice that although the maximum value of the maximand may be well defined, b is not usually uniquely estimated in a finite data set, because values of b near betahat would make the same predictions. Often, however, b is estimated within a narrow range. (Econterms)

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