The problem of statistical parameter estimation is considered for binary GLM-based autoregression with the link function of general form and the base functions (regressors) nonlinear w.r.t. the lagged variables. A new consistent asymptotically normal frequencies-based estimator (FBE) is constructed and compared with the classical MLE. It is shown that the FBE has less restrictive sufficient conditions of uniqueness than the MLE (does not need log-concavity of the inverse link) and can be computed recursively under the model extension. The sparse version of the FBE is proposed and the optimal model-dependent weight matrices (parameterizing the FBE) are found for the FBE and for the sparse FBE. The proposed empirical choice of the subset of s-tuples for the sparse FBE is examined by numerical and analytical examples. Computer experiments for comparison of the FBE versus the MLE are performed on simulated and real (genetic) data.

中文翻译：

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二元条件非线性自回归时间序列参数的统计估计

对于具有通用形式的链接函数和具有滞后变量的非线性的基函数（回归变量）的基于二进制GLM的自回归，考虑了统计参数估计的问题。构造了一个新的一致渐近正态基于频率的估计器（FBE），并将其与经典MLE进行了比较。结果表明，与MLE相比，FBE具有较少的唯一性约束条件（不需要逆链路的对数凹度），并且可以在模型扩展下递归计算。提出了FBE的稀疏版本，并找到了FBE和稀疏FBE的最佳模型相关权重矩阵（参数化FBE）。通过数值和分析实例，对稀疏FBE的s元组子集的经验选择进行了研究。