Purpose: The purpose of this paper is to propose a novel curvilinear path estimation model employing multivariate adaptive regression splines (MARS) for mid vehicle collision avoidance. The two-phase path estimation scheme initially uses the offset (position) value of the front and the mid (host) vehicle to build the crisp model. The resulting crisp model is MARS regressed to deliver a closely aligned actual model in the second phase. This arrangement significantly narrows the gap between the estimated and the true path analyzed using the mean square error (MSE) for different offsets on Next Generation Simulation Interstate 80 (NGSIM I-80) data set. The presented model also covers parallel parking by encompassing the reverse motion of the host vehicle in the path estimation, thereby, making it amicable for real-road scenarios. Design/methodology/approach: The two-phase path estimation scheme initially uses the offset (position) value of the front and the mid (host) vehicle to build the crisp model. The resulting crisp model is MARS regressed to deliver a closely aligned actual model in the second phase. Findings: This arrangement significantly narrows the gap between the estimated and the true path studied using MSE for different offsets on real (Next Generation Simulation-NGSIM) data. The presented model also covers parallel parking by encompassing the reverse motion of the host vehicle in the path estimation. Thereby, making it amicable for real-road scenarios. Originality/value: This paper builds a mathematical model that considers the offset and host (mid) vehicles for appropriate path fitting. © 2019, Emerald Publishing Limited.