Mendelian Randomization (MR) has been widely applied to infer causality of exposures on outcomes in the genome wide association (GWAS) era. Existing approaches are often subject to biases from multiple sources including weak instruments, sample overlap, and measurement error. We introduce MRBEE, a computationally efficient multivariable MR method that can correct for all known biases simultaneously, which is demonstrated in theory, simulations, and real data analysis. In comparison, all existing MR methods are biased. In two independent real data analyses, we observed that the causal effect of BMI on coronary artery disease risk is completely mediated by blood pressure, and that existing MR methods drastically underestimate the causal effect of cannabis use disorder on schizophrenia risk compared to MRBEE. We demonstrate that MRBEE can be a useful tool in studying causality between multiple risk factors and a disease outcome, especially as more GWAS summary statistics are being made publicly available.

Mendelian Randomization (MR) has been widely applied to infer causality of exposures on outcomes in the genome wide association (GWAS) era. Existing approaches are often subject to biases from multiple sources including weak instruments, sample overlap, and measurement error. We introduce MRBEE, a computationally efficient multivariable MR method that can correct for all known biases simultaneously, which is demonstrated in theory, simulations, and real data analysis. In comparison, all existing MR methods are biased. In two independent real data analyses, we observed that the causal effect of BMI on coronary artery disease risk is completely mediated by blood pressure, and that existing MR methods drastically underestimate the causal effect of cannabis use disorder on schizophrenia risk compared to MRBEE. We demonstrate that MRBEE can be a useful tool in studying causality between multiple risk factors and a disease outcome, especially as more GWAS summary statistics are being made publicly available.

The estimation of large functional and longitudinal data, which refers to the estimation of mean function, estimation of covariance function, and prediction of individual trajectory, is one of the most challenging problems in the field of high-dimensional statistics. Functional Principal Components Analysis (FPCA) and Functional Linear Mixed Model (FLMM) are two major statistical tools used to address the estimation of large functional and longitudinal data; however, the former suffers from a dramatically increasing computational burden while the latter does not have clear asymptotic properties. In this paper, we propose a computationally effective estimator of large functional and longitudinal data within the framework of FLMM, in which all the parameters can be automatically estimated. Under certain regularity assumptions, we prove that the mean function estimation and individual trajectory prediction reach the minimax lower bounds of all nonparametric estimations. Through numerous simulations and real data analysis, we show that our new estimator outperforms the traditional FPCA in terms of mean function estimation, individual trajectory prediction, variance estimation, covariance function estimation, and computational effectiveness.

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Carbon price fluctuations significantly impact the development of industries, energy, agriculture, and stock investments. The carbon price possesses the features of nonlinearity, non-stationarity, and high complexity as a time series. To overcome the negative impact of these characteristics on prediction and to improve the prediction accuracy of carbon price series, a combination prediction model named Lp-CNN-LSTM, which utilizes both convolutional neural networks and long short-term memory networks, has been proposed. Strategy one involved establishing distinct models of CNN-LSTM and LSTM to analyze high-frequency and low-frequency carbon price sequences; the combination of output was integrated to predict carbon prices more precisely. Strategy two comprehensively considered the economic and technical indicators of carbon price sequences based on the Pearson correlation coefficient, while the Multi-CNN-LSTM model selected explanatory variables that strongly correlated with carbon prices. Finally, a predictive model for a combination of carbon prices was developed using Lp-norm. The empirical study focused on China’s major carbon markets, including Hubei, Guangdong, and Shanghai. According to the error indicators, the performance of the Lp-CNN-LSTM model was superior to individual strategy prediction models. The Lp-CNN-LSTM model has excellent accuracy, superiority, and robustness in predicting carbon prices, which can provide a necessary basis for revising carbon pricing strategies, regulating carbon trading markets, and making investment decisions.