Comparing Heritability Estimators under Alternative Structures of Linkage Disequilibrium

SNP heritability of a trait is the proportion of its variance explained by the additive effects of the genome-wide single nucleotide polymorphisms (SNPs). The existing approaches to estimate SNP heritability can be broadly classified into two categories. One set of approaches model the SNP effects as fixed effects and the other treats the SNP effects as random effects. These methods make certain assumptions about the dependency among individuals (familial relationship) as well as the dependency among markers (linkage disequilibrium, LD) to provide consistent estimates of SNP heritability as the number of individuals increases. While various approaches have been proposed to account for such dependencies, it remains unclear which estimates reported in the literature are more robust against various model mis-specifications. Here we investigate the impact of different structures of LD and familial relatedness on heritability estimation. We show that the performance of different methods for heritability estimation depends heavily on the structure of the underlying pattern of LD and the degree of relatedness among sampled individuals. However, contrary to the claim in the current literature, we did not find significant differences in the performance of these fixed-SNP-effects and random-SNP-effects approaches. Moreover, we established the equivalence between the two method-of-moments estimators, one from each of these two lines of approaches.

Multiple directorships and earnings quality: Does investor protection matter?

Purpose This study aims to investigate whether higher earnings quality is related to the existence of multiple directorships among corporate boards and whether this relationship varies with the quality of investor protection. Design/methodology/approach This paper used a dynamic panel data modelling on the sample of 2,090 firm-year observations over the period from 2007 to 2016 in Malaysia. The generalized method of moments estimators were used to deal with endogeneity and other econometric problems. Findings This study finds that the accumulation of several outside directorships is negatively associated with the firm's earnings quality, as measured by the magnitude of discretionary accruals. More importantly, the findings provide evidence that multiple directors are more efficient in improving earnings quality in healthy investor protection environment. Practical implications The appointment of directors should be based on market-based and not on a relationship (i.e. financial and industry professionals). Originality/value The results highlight the importance of interaction between internal and external governance mechanisms to improve the firm's financial performance, investment and market efficiency. High-quality investor protection and law enforcement are significant for enhancing the monitoring role of multiple directorships in improving earnings quality.

Assortative Mating Biases Marker-based Heritability Estimators

Many complex traits are subject to assortative mating (AM), with recent molecular genetic findings confirming longstanding theoretical predictions that AM alters genetic architecture by inducing long range dependence across causal variants. However, all marker-based heritability estimators assume mating is random. We provide mathematical and simulation-based evidence demonstrating that both method-of-moments estimators and likelihood-based estimators produce biased estimates in the presence of AM and that common approaches to account for population structure fail to mitigate this bias. Then, examining height and educational attainment in the UK Biobank, we demonstrate that these biases affect real world traits. Finally, we derive corrected heritability estimators for traits under equilibrium AM.

Estimating FST and kinship for arbitrary population structures

FST and kinship are key parameters often estimated in modern population genetics studies in order to quantitatively characterize structure and relatedness. Kinship matrices have also become a fundamental quantity used in genome-wide association studies and heritability estimation. The most frequently-used estimators of FST and kinship are method-of-moments estimators whose accuracies depend strongly on the existence of simple underlying forms of structure, such as the independent subpopulations model of non-overlapping, independently evolving subpopulations. However, modern data sets have revealed that these simple models of structure likely do not hold in many populations, including humans. In this work, we analyze the behavior of these estimators in the presence of arbitrarily-complex population structures, which results in an improved estimation framework specifically designed for arbitrary population structures. After generalizing the definition of FST to arbitrary population structures and establishing a framework for assessing bias and consistency of genome-wide estimators, we calculate the accuracy of existing FST and kinship estimators under arbitrary population structures, characterizing biases and estimation challenges unobserved under their originally-assumed models of structure. We then present our new approach, which consistently estimates kinship and FST when the minimum kinship value in the dataset is estimated consistently. We illustrate our results using simulated genotypes from an admixture model, constructing a one-dimensional geographic scenario that departs nontrivially from the independent subpopulations model. Our simulations reveal the potential for severe biases in estimates of existing approaches that are overcome by our new framework. This work may significantly improve future analyses that rely on accurate kinship and FST estimates.

A Comparison Between Two Shape Parameters Estimators for (Burr-XII) Distribution

This paper deals with defining Burr-XII, and how to obtain its p.d.f., and CDF, since this distribution is one of failure distribution which is compound distribution from two failure models which are Gamma model and weibull model. Some equipment may have many important parts and the probability distributions representing which may be of different types, so found that Burr by its different compound formulas is the best model to be studied, and estimated its parameter to compute the mean time to failure rate. Here Burr-XII rather than other models is consider because it is used to model a wide variety of phenomena including crop prices, household income, option market price distributions, risk and travel time. It has two shape-parameters (α, r) and one scale parameter (λ) which is considered known. So, this paper defines the p.d.f. and CDF and derives its Moments formula about origin, and also derive the Moments estimators of two shapes parameters (α, r) in addition to maximum likelihood estimators as well as percentile estimators, the scale parameter (λ) is not estimated (as it is considered known). The comparison between three methods is done through simulation procedure taking different sample size (n=30, 60, 90) and different sets of initial values for (α, r, λ).It is observed that the moment estimators are the best estimator with percentage (46%) ,(42%) respectively compared with other estimators.

A Power Maxwell Distribution with Heavy Tails and Applications

In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.

The joint impact of infrastructure and institutions on economic growth

This paper examines the joint impact of infrastructure capital and institutional quality on economic growth using a large panel dataset covering 99 countries and spanning the years 1980–2015. The empirical strategy involves estimating a simple growth model where, in addition to standard controls, infrastructure, institutional quality, and their interaction are included as explanatory variables. Potential endogeneity concerns are addressed by employing generalized method of moments estimators that utilize internal instruments. We find that the interaction terms between infrastructure capital and institutional quality show a positive and significant impact on economic growth. These results are robust to a variety of alternative specifications and institutional quality measures. Hence, our results suggest that maximizing returns from infrastructure capital requires improving the quality of institutions.