The linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper.

线性校准模型是一种强大的统计工具，可用于通过代理观察来预测未知响应变量Y或预测变量，X。由于校准涉及基于有限数量的噪声数据估计回归模型参数，因此无偏校准斜率估计至关重要。这可以通过最先进的数据驱动统计技术来实现。本文表明，两个变量估计的加权最小二乘法（WLSXY）能够在异方差下提供无偏斜率估计。在同方差的情况下，除了 WLSXY 之外，带有偏差校正的普通最小二乘（OLS）估计（OLSBC）也表现良好。为了实现无偏，还需要采取正确的回归方向（即 Y 在 X) 考虑在内。本文介绍了一种成对移动块自举重采样方法，用于在真实气候条件下（即噪声分量中的非高斯分布形状和自相关）获得准确的估计置信区间（CI）。蒙特卡洛模拟实验验证了该方法的可行性和有效性。参数估计和引导复制用于预测 CI 的响应。针对海面温度和珊瑚氧同位素组成的配对时间序列数据集说明了无偏校准的方法。本文随附具有 OLSBC 和 WLSXY 实现的 Fortran 软件。