# Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

### Abstract

In this research paper, we set forward a non-parametric multivariate recursive kernel regression estimator under missing data using the propensity score approach in order to describe writing word production. Our main objective is to explore cognitive processes and mental representations mobilized when a human being prepares to write a word according to the idea developed in Perret and Olive (2019). We investigate the asymptotic properties of the proposed recursive estimator and compare them to the well known Nadaraya-Watson's regression estimator. We calculate the bias and the variance of the proposed estimator which depend on the choice of some parameters such as the stepsize and the bandwidth. We examine some data-driven procedures to select these parameters. Thus, we demonstrate that, under some optimal choices of these parameters, the MSE (Mean Squared Error) of the proposed estimator can be smaller than the one obtained by using Nadaraya Watson's regression estimator. The elaborated estimator is then applied to the behavioral data to classify some participants in groups. This classication may stand for a departure point to tackle written behavior variations.### References

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*Statistics, Optimization & Information Computing*,

*10*(4), 1021-1043. https://doi.org/10.19139/soic-2310-5070-1507

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