The goal of this paper is to provide some statistical tools for nonparametric estimation and inference in psychological and economic experiments. We consider a framework in which a quantity of interest depends on some primitives through an unknown function f. An estimator of this unknown function can be obtained from a controlled experiment in which n subjects are gathered, and a vector of stimuli is administered to each subject who provides a set of T responses . We propose to estimate f nonparametrically using the method of sieves. We provide conditions for consistency of this estimator when either n or T or both divergeto infinity, and when the answers of each subject are correlated and this correlation differs across subjects. We further demonstrate that the rate of convergence depends upon the covariance structure of the error term taken across individuals. A convergence rate is also obtained for derivatives. These results allow us to derive the optimal divergence rate of the dimension of the sieve basis with both n and T and thus provide guidance about the optimal balance between the number of subjects and the number of questions in a laboratory experiment . We argue that in general a large value of n is better than a large value of T. Conditions for asymptotic normality of linear and nonlinear functionals of the estimated function of interest are derived. These results are further applied to obtain the asymptotic distribution of the Wald test when the number of constraints under the null is finite and when it diverges to infinity along with other asymptotic parameters. Lastly, we investigate the properties of the previous test when the conditional covariance matrix is replaced by a consistent estimator.
The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of nsubjects provides T responses to a vector of T stimuli . We propose to estimate the unknown function f linking stimuli to responses through a nonparametric sieve estimator. We give conditions for consistency when either nor Tor both diverge. The rate of convergence depends upon the error covariance structure, that is allowed to differ across subjects. With these results we derive the optimal divergence rate of the dimension of the sieve basis with both n and T . We provide guidance about the optimal balance between the number of subjects and questions in a laboratory experiment and argue that a large nis often better than a large T. We derive conditions for asymptotic normality of functionals of the estimator of Tand apply them to obtain the asymptotic distribution of the Wald test when the number of constraints under the null is finite and when it diverges along with other asymptotic parameters. Lastly, we investigate the previous properties when the conditional covariance matrix is replaced by an estimator.
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