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• Parental investment and skill mediate caregiver mental health and child development. • Caregiver depression are more harmful to parenting practices and child development. • The variety of play material has significant mediation effect on child development. • Coercive parenting mediate caregiver mental health and child development. Parenting practices are associated with early childhood development (ECD), and some evidences suggest that mental health might affect parenting practices. However, the interrelationships of mental health, parenting practices, and ECD outcomes have not yet been well documented in developing contexts like rural China. This paper aims to investigate the interrelationships between the caregiver's mental health, parenting practices, and the child's ECD outcomes in rural China. A total of 1787 sample households in an undeveloped rural area of western China are enrolled in the study. A socioeconomic questionnaire, the Depression, Anxiety and Stress Scale, the Family Care Indicators, the Parent and Family Adjustment Scales, and the Bayley Scales of Infant Development version III were used to measure the socioeconomic characteristics of sample households, the caregiver's mental health, parental investments and parenting skills, and the child's development outcomes, respectively. Mediation model was then applied to estimate the interrelationships. The results showed that parental practices significantly mediated between the caregiver's mental health and the child's cognition, language, motor, and social–emotion development. Through parental investments, one standard deviation increases in the caregiver's mental health test score was associated with the decline in the child's four development scores by 0.6% standard deviation, respectively. Through parenting skills, one standard deviation increases in the caregiver's mental health test score was associated with the decline in the child's language and social-emotional score by 2% and 5% standard deviation, respectively. Different dimensions of caregiver mental health, parental investments and skills played heterogeneous roles in the interrelationships. Early interventions aimed at improving the caregiver's mental health, parental investments and skills are important and might be effective to improve early childhood development in rural China. [ABSTRACT FROM AUTHOR]

• Parental belief is associated with Child social-emotional development. • Parental investments mediate parental belief and child development. • The mediation effects vary across investments and developmental outcomes. • The varieties of play materials and activities are the strongest mediators. Parental investments are associated with early child outcomes, and some evidences outside China suggest that parental belief might affect parental investments. However, the interrelationships of parental belief, parental investments, and early child development has not been well documented in China. This paper aims to study the interrelationships between the caregiver's parental belief, the caregiver's parental investments, and the child's early developmental outcomes in rural China. A total of 1787 sample households in an undeveloped rural area of western China are enrolled in the cross-sectional study. A parental belief questionnaire, the Family Care Indicators (FCI), the Bayley Scales of Infant Development version III (BSID-III), and a socioeconomic questionnaire were used to measure the caregiver's parental belief on parenting practices, the caregiver's parental investments, the child's early developmental outcomes, and the socioeconomic characteristics of sample households, respectively. The mediation model was then applied to estimate the interrelationships. The results find that the caregiver's parental investments significantly mediate in the relationships between the caregiver's parental belief and the child's early developmental outcomes. Through parental investments, one standard deviation (SD) increase in the caregiver's parental belief is corresponding to 3% of one SD increase in the child's four developmental outcomes (cognition, language, motor, and social–emotion) respectively. For future studies aimed at designing targeted interventions on early child development in rural China, the key findings of this paper might be informative. Early interventions aimed at strengthening the caregiver's subjective belief on parenting practices and increasing the parental investments in the household might be effective to improve the development of rural children. [ABSTRACT FROM AUTHOR]

• A portfolio selection problem with higher-order moments is considered. • Machine learning algorithms are applied for data analysis and prediction in the stock market. • Genetic algorithm is used to solve the multi-objective optimization problem. • The out-of-sample performance of our model is significantly better than those of traditional ones. • Robustness is checked, compared with another two existing methods. Skewness and kurtosis, the third and fourth order moments, are statistics to summarize the shape of a distribution function. Recent studies show that investors would take these higher-order moments into consideration to make a profitable investment decision. Unfortunately, due to the difficulties in solving the multi-objective problem with higher-order moments, the literature on portfolio selection problem with higher-order moments is few. This paper proposes a new hybrid approach to solve the portfolio selection problem with skewness and kurtosis, which includes not only the multi-objective optimization but also the data-driven asset selection and return prediction, where the techniques of two-stage clustering, radial basis function neural network and genetic algorithm are employed. With the historical data from Shanghai stock exchange, we find that the out-of-sample performance of our model with higher-order moments is significantly better than that of traditional mean-variance model and verify the robustness of our hybrid algorithm. [ABSTRACT FROM AUTHOR]

• It is unclear that what delivery model of early childhood interventions may be most effective in developing countries. • We evaluate the effects of a center-based parenting intervention on early development and parenting practices in rural China. • We compare the effects to a home-based intervention using the same curriculum and public service system in the same region. • We find the home-visiting intervention was more effective than the center-based parenting intervention on child outcomes. • The difference in effects appears to be driven by different patterns of compliance. We present the results of a cluster-randomized controlled trial that evaluates the effects of a free, center-based parenting intervention on early cognitive development and parenting practices in 100 rural villages in China. We then compare these effects to a previous trial of a home-based intervention conducted in the same region, using the same parenting curriculum and public service system, accounting for potential differences between the studies. We find that the center-based intervention did not have a significant impact on child development outcomes, but did lead to increases in the material investments, time investments, and parenting skills of caregivers. The average impact of the center-based intervention on child skills and investments in children was significantly smaller than the home-visiting intervention. Analysis of the possible mechanisms suggests that the difference in effects was driven primarily by different patterns of selection into program participation. [ABSTRACT FROM AUTHOR]