Pooling test statistics across multiply imputed datasets for nonnormal items

In structural equation modeling, when multiple imputation is used for handling missing data, model fit evaluation involves pooling likelihood-ratio test statistics across imputations. Under the normality assumption, the two most popular pooling approaches were proposed by Li et al. (Statistica Sinica, 1(1), 65-92, 1991) and Meng and Rubin (Biometrika, 79(1), 103-111, 1992). When the assumption of normality is violated, it is not clear how well these pooling approaches work with the test statistics generated from various robust estimators and multiple imputation methods. Jorgensen and colleagues (2021) implemented these pooling approaches in their R package semTools; however, no systematical evaluation has been conducted. In this simulation study, we examine the performance of these approaches in working with different imputation methods and robust estimators under nonnormality. We found that the naïve pooling approach based on Meng and Rubin (Biometrika, 79(1), 103-111, 1992; D3SN) worked the best when combining with the normal-theory-based imputation and either MLM or MLMV estimator.

A discussion on the robust vector autoregressive models: novel evidence from safe haven assets

The vector autoregressive (VAR) model has been popularly employed in operational practice to study multivariate time series. Despite its usefulness in providing associated metrics such as the impulse response function (IRF) and forecast error variance decomposition (FEVD), the traditional VAR model estimated via the usual ordinary least squares is vulnerable to outliers. To handle potential outliers in multivariate time series, this paper investigates two robust estimation methods of the VAR model, the reweighted multivariate least trimmed squares and the multivariate MM-estimation. The robust information criteria are also proposed to select the appropriate number of temporal lags. Via extensive simulation studies, we show that the robust VAR models lead to much more accurate estimates than the original VAR in the presence of outliers. Our empirical results include logged daily realized volatilities of six common safe haven assets: futures of gold, silver, Brent oil and West Texas Intermediate (WTI) oil and currencies of Swiss Francs and Japanese Yen. Our sample covers July 2017-June 2020, which includes the history-writing price drop of WTI on April 20, 2020. Our baseline results suggest that the traditional VAR model may significantly overestimate some parameters, as well as IRF and FEVD metrics. In contrast, robust VAR models provide more reliable results, the validity of which is verified via various approaches. Empirical implications based on robust estimates are further illustrated.

Does combined heat and power mitigate CO2 emissions? A cross-country analysis

Combined heat and power (CHP), which produces both heat and electricity at the same time, is so efficient that it can reduce energy use and emit less carbon dioxide (CO₂) than conventional fossil fuel use. This article attempts to look empirically into the impact of CHP share in total electricity generation on CO₂ emissions in a cross-country context. Data from 35 countries during the period 2009-2015 are used. For this purpose, the variable of CO₂ emissions is regressed on three variables of constant, gross domestic product, and CHP share using two robust estimators. The results show that the level of CHP share of a country affects the level of its CO₂ emissions negatively. That is, CHP leads to less CO₂ emissions.

Robust state estimation of feeding-blending systems in continuous pharmaceutical manufacturing

State estimation is a fundamental part of monitoring, control, and real-time optimization in continuous pharmaceutical manufacturing. For nonlinear dynamic systems with hard constraints, moving horizon estimation (MHE) can estimate the current state by solving a well-defined optimization problem where process complexities are explicitly considered as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, state estimates can be unreliable if noise is not normally distributed or measurements are contaminated with gross or systematic errors. To improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE framework. The proposed MHE approach is implemented on two pharmaceutical continuous feeding-blending system (FBS) configurations which include loss-in-weight (LIW) feeders and continuous blenders. Numerical results show that our MHE approach is robust to gross errors and can provide reliable state estimates when measurements are contaminated with outliers and drifts. Moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.

Robust Fitting of a Weibull Model with Optional Censoring

The Weibull family is widely used to model failure data, or lifetime data, although the classical two-parameter Weibull distribution is limited to positive data and monotone failure rate. The parameters of the Weibull model are commonly obtained by maximum likelihood estimation; however, it is well-known that this estimator is not robust when dealing with contaminated data. A new robust procedure is introduced to fit a Weibull model by using L₂ distance, i.e. integrated square distance, of the Weibull probability density function. The Weibull model is augmented with a weight parameter to robustly deal with contaminated data. Results comparing a maximum likelihood estimator with an L₂ estimator are given in this article, based on both simulated and real data sets. It is shown that this new L₂ parametric estimation method is more robust and does a better job than maximum likelihood in the newly proposed Weibull model when data are contaminated. The same preference for L₂ distance criterion and the new Weibull model also happens for right-censored data with contamination.