We describe the R package EstemPMM, which implements the Polynomial Maximization Method (PMM) for parameter estimation under non-Gaussian errors. PMM exploits higher-order cumulants of the error distribution -- specifically the third standardized moment gamma_3 and fourth standardized moment gamma_4 -- to construct estimators that outperform ordinary least squares (OLS) whenever the errors are asymmetric or leptokurtic. The package provides a unified interface for linear regression (lm_pmm2, lm_pmm3), autoregressive and moving-average time-series models (ar_pmm2, ma_pmm2, arma_pmm2, arima_pmm2, and seasonal variants), a data-driven dispatch function (pmm_dispatch) that automatically selects OLS, PMM2, or PMM3 based on the sample skewness and excess kurtosis, and Monte Carlo comparison utilities. The implementation uses R's S4 class system and follows standard generic interfaces (coef, fitted, residuals, predict, summary, AIC, logLik, vcov, confint). Asymptotic efficiency is characterised by Kunchenko-style coefficients g_2, g_3 in [0,1], defined as the ratios of the asymptotic variance of the PMM2 and PMM3 estimators to that of OLS. Monte Carlo experiments confirm the theoretical values and a WTI crude-oil case study illustrates the dispatcher and parameter-precision benefits of PMM2 on real heavy-tailed data. EstemPMM version 0.3.2 is available from CRAN at https://CRAN.R-project.org/package=EstemPMM under the GPL-3 licence.

翻译：[译摘要] 本文介绍R语言包EstemPMM，其实现了非高斯误差下参数估计的多项式最大化方法(PMM)。PMM利用误差分布的高阶累积量——具体为三阶标准化矩gamma_3与四阶标准化矩gamma_4——构建估计量，在误差呈不对称或尖峰分布时优于普通最小二乘法(OLS)。该包提供统一接口用于线性回归(lm_pmm2, lm_pmm3)、自回归与滑动平均时间序列模型(ar_pmm2, ma_pmm2, arma_pmm2, arima_pmm2及季节性变体)，以及基于样本偏度和超额峰度自动选择OLS、PMM2或PMM3的数据驱动调度函数(pmm_dispatch)，并包含蒙特卡洛比较实用程序。实现采用R语言的S4类系统，遵循标准泛型接口(coef、fitted、 residuals、predict、summary、AIC、logLik、vcov、confint)。渐近效率由Kunchenko型系数g_2、g_3（定义于[0,1]区间）刻画，即PMM2和PMM3估计量渐近方差与OLS估计量渐近方差之比。蒙特卡洛实验验证了理论值，WTI原油案例研究展示了调度函数与PMM2在真实重尾数据上的参数精度优势。EstemPMM 0.3.2版已发布于CRAN(https://CRAN.R-project.org/package=EstemPMM)，遵循GPL-3许可协议。