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\section{Robustness Checks}
\label{sec:robustness}
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We conduct several robustness checks to assess the stability of our main findings.

\subsection{Sensitivity to Spatial Weights Specification}

Table~\ref{tab:sensitivity_k} reports the spatial lag parameter $\rho$ at $\tau = 0.50$ for single-family houses under alternative KNN specifications. The results are qualitatively stable: $\rho$ ranges from 0.26 to 0.31 across $K \in \{5, 10, 15, 20\}$, and the amenity coefficient rankings are preserved. The most notable sensitivity is that the park coefficient becomes insignificant at the median when $K = 20$, reflecting the dilution of local park effects when the neighbor set is expanded. We retain $K = 10$ as our baseline, following the spatial hedonic convention \citep{pace2004spatial}.

\input{tables/sensitivity_k}

\subsection{Bootstrap Replications}

We compare standard errors obtained with $B = 200$ and $B = 500$ bootstrap replications for the house segment. The maximum relative difference in bootstrap standard errors is 8\%, and no amenity variable changes significance status. This confirms that $B = 200$ provides adequate precision for our inference \citep{efron1994introduction}.

\subsection{Alternative Trimming Thresholds}

We re-estimate the house model using 1\%/99\% and 2\%/98\% trimming (instead of our baseline 0.5\%/99.5\%). The amenity coefficient trajectories across quantiles are preserved, though the extreme quantile estimates ($\tau = 0.10$ and $\tau = 0.90$) show more sensitivity to trimming, as expected. The hospital sign reversal and highway declining gradient are robust to all trimming specifications.

\subsection{Subsample Stability}

We split the house sample geographically into Montreal metro ($N = 1{,}180$) and non-Montreal ($N = 5{,}070$) subsamples. The key findings---declining highway gradient, hospital sign reversal, and declining transit premium---are qualitatively present in both subsamples, though the non-Montreal sample shows larger highway and transit coefficients (reflecting greater accessibility dependence in regional markets) and stronger spatial autocorrelation (Moran's $I = 0.55$ vs.\ 0.42).

\subsection{Listing Price vs.\ Transaction Price Concern}

While we cannot directly assess the bias from using listing prices, we note three mitigating factors. First, the hedonic coefficients are identified from cross-sectional variation in amenity access conditional on all other attributes; unless the listing premium varies systematically with amenity proximity (conditional on price level, location, and structural characteristics), the coefficients are unbiased. Second, the spatial lag partially absorbs any neighborhood-level variation in listing strategy. Third, our quantile regression approach is more robust to distributional misspecification than OLS \citep{koenker2005quantile}, which is relevant if the listing-to-sale ratio varies across the price distribution.