We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite-sample performance of our method and compare it with existing methods. Our method can be extended to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points.

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Background Hypertension remains a leading global cause for premature death and disease. Most treatment guidelines emphasize the importance of risk factors, but not all are known, modifiable, or easily avoided. Population blood pressure correlates with latitude and is lower in summer than winter. Seasonal variations in sunlight exposure account for these differences, with temperature believed to be the main contributor. Recent research indicates that UV light enhances nitric oxide availability by mobilizing storage forms in the skin, suggesting incident solar UV radiation may lower blood pressure. We tested this hypothesis by exploring the association between environmental UV exposure and systolic blood pressure ( SBP ) in a large cohort of chronic hemodialysis patients in whom SBP is determined regularly. Methods and Results We studied 342 457 patients (36% black, 64% white) at 2178 US dialysis centers over 3 years. Incident UV radiation and temperature data for each clinic location were retrieved from the National Oceanic and Atmospheric Administration database. Linear mixed effects models with adjustment for ambient temperature, sex/age, body mass index, serum Na + /K + and other covariates were fitted to each location and combined estimates of associations calculated using the DerSimonian and Laird procedure. Pre‐dialysis SBP varied by season and was ≈4 mm Hg higher in black patients. Temperature, UVA and UVB were all linearly and inversely associated with SBP . This relationship remained statistically significant after correcting for temperature. Conclusions In hemodialysis patients, in addition to environmental temperature, incident solar UV radiation is associated with lower SBP . This raises the possibility that insufficient sunlight is a new risk factor for hypertension, perhaps even in the general population.

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