<![CDATA[Nonparametric regression is frequently applied to describe the connection between variables when the functional form is not defined. The Fourier series estimator is especially effective in capturing periodic patterns in regression curves. In multivariable cases, however, strong correlations among predictor variables often lead to multicollinearity, which results in unstable parameter estimation due to the near-singularity of the design matrix. While the Fourier approach has been widely developed for curve estimation, its theoretical framework has not explicitly accommodated this issue. This research introduces a ridge–Fourier series estimator for nonparametric regression to achieve stable parameter estimation in the presence of multicollinearity. The estimator is derived under a penalized likelihood framework by incorporating a ridge penalty into the Fourier series model and optimizing it using Maximum Likelihood Estimation (MLE). This approach yields a closed-form estimator with reduced variance and improved numerical stability while retaining the flexibility of the nonparametric structure. The oscillation parameter and ridge penalty parameter are determined through the Generalized Cross Validation (GCV) criterion to achieve an optimal smoothing level. This research's major contribution involves the theoretical formulation and derivation of the ridge–Fourier series estimator within the additive nonparametric regression model.]]>
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