Evaluation of Gaussian orthant probabilities based on orthogonal projections to subspaces

In this paper, a new procedure is described for evaluating the probability that all elements of a normally distributed vector are non-negative, which is called the non-centered orthant probability. This probability is defined by a multivariate integral of the density function. The definition is simple, and this probability arises frequently in statistics because the normal distribution is prevalent. The method for evaluating this probability, however, is not obvious, because applying direct numerical integration is not practical except in low dimensional cases. In the procedure proposed in this paper, the problem is decomposed into sub-problems of lower dimension. Considering the projection onto subspaces, the solutions of the sub-problems can be shared in the evaluation of higher dimensional problems. Thus the sub-problems form a lattice structure. This reduces the computational time from a factorial order, where the interim results are not shared, to order \(p^{2}2^{p}\), which is faster than the procedures that have been reported in the literature.     

Japanese Children’s Knowledge of the Facial Components of Basic Emotions

While numerous studies have investigated children’s recognition of facial emotional expressions, little evidence has been gathered concerning their explicit knowledge of the components included in such expressions. Thus, we investigated children’s knowledge of the facial components involved in the expressions of happiness, sadness, anger, and surprise. Four- and 5-year-old Japanese children were presented with the blank face of a young character, and asked to select facial components in order to depict the emotions he felt. Children’s overall performance in the task increased as a function of age, and was above chance level for each emotion in both age groups. Children were likely to select the Cheek raiser and Lip corner puller to depict happiness, the Inner brow raiser, Brow lowerer, and Lid droop to depict sadness, the Brow lowerer and Upper lid raiser to depict anger, and the Upper lid raiser and Jaw drop to depict surprise. Furthermore, older children demonstrated a better knowledge of the involvement of the Upper lid raiser in surprise expressions.     

Adaptation and validation of the Japanese version of the Gambling Urge Scale

In Japan, accurately assessing and targeting gambling urges is important for the treatment of gambling disorder because people are constantly exposed to external triggers that elicit gambling urges. However, a valid measure that assesses gambling urges has not been adequately established. Therefore, the purpose of this study was to examine the psychometric properties of the Japanese version of the Gambling Urge Scale (GUS-J), which is a well-known valid 6-item instrument in English-speaking countries. Two hundred and thirty-nine participants completed questionnaires, 86 of which met the criteria for a probable gambling disorder. As with the original GUS, the GUS-J was demonstrated to be a one-factor model that accounted for 63.82% of the total item variance, with all items demonstrating loadings of .40 or higher. With regard to reliability, the GUS-J showed good internal consistency (α = .88). Furthermore, validity based on evidence of relationships with other variables, especially convergent and concurrent validity of the GUS-J, were supported by several analyses that examined hypotheses based on previous findings. In conclusion, this study showed that the GUS-J has good psychometric properties as an assessment tool for gambling urges in Japanese people and it will be useful for future clinical practice and research.     

On the almost unbiased ridge regression estimator

The purpose of this paper is two-fold. One is to compare the almost unbiased generalized ridge regression (AUGRR) estimator proposed by Singh, Chaubey and Dwivedi (1986) with the generalized ridge regression (GRR) estimator and with the ordinary least squares (OLS) estimator in terms of the mean squared error criterion. Second is to examine small sample properties of the operational almost unbiased ordinary ridge regression (AUORR) estimator by Monte Carlo experiments.     

A note on combining ridge and principal component regression

Baye and Parker (1984) proposed the r-k class estimator. The purpose of this note is to deal with the comparisons among the r-k class estimators in terms of the mean square error criterion.     

Estimation of the average causal effect via multiple propensity score stratification

Suppose we are interested in estimating the average causal effect (ACE) for the population mean from observational study. Because of simplicity and ease of interpretation, stratification by a propensity score (PS) is widely used to adjust for influence of confounding factors in estimation of the ACE. Appropriateness of the estimation by the PS stratification relies on correct specification of the PS. We propose an estimator based on stratification with multiple PS models by clustering techniques instead of model selection. If one of them correctly specifies, the proposed estimator removes bias and thus is more robust than the standard PS stratification.     

Prenatal Depression and Infant Temperament: The Moderating Role of Placental Gene Expression

Prior research has demonstrated the link between maternal depression during pregnancy (i.e., prenatal depression) and increased neurodevelopmental dysregulation in offspring. However, little is known about the roles of key hypothalamic–pituitary axis regulatory genes in the placenta modulating this association. This study will examine whether placental gene expression levels of 11β‐hydroxysteroid dehydrogenase type 2 (HSD11B2), glucocorticoid receptor (NR3C1), and mineralocorticoid receptor (NR3C2) can help elucidate the underlying mechanisms linking prenatal depression to infant temperament, particularly in infants with high negativity and low emotion regulation. Stored placenta tissues (N = 153) were used to quantify messenger ribonucleic acid levels of HSD11B2, NR3C1, and NR3C2. Assessments of prenatal depression and infant temperament at 6 months of age were ascertained via maternal report. Results found that prenatal depression was associated with increased Negative Affectivity (p < .05) after controlling for postnatal depression and psychosocial characteristics. Furthermore, the association between prenatal depression and Negative Affectivity was moderated by gene expression levels of HSD11B2, NR3C1, and NR3C2 such that greater gene expression significantly lessened the association between prenatal depression and Negative Affectivity. Our findings suggest that individual differences in placental gene expression may be used as an early marker of susceptibility or resilience to prenatal adversity.     

Orthant probabilities of elliptical distributions from orthogonal projections to subspaces

Statistics and Computing - A new procedure is proposed for evaluating non-centred orthant probabilities of elliptical distributed vectors, which is the probabilities that all elements of a vector...     

On exact small sample properties of the minimax generalized ridge regression estimators

The purpose of this paper is to compare sampling performance of the minimax generalized ridge regression estimators considered by Casella (1985) with that of ordinary least squares estimator by numerical calculations of exact mean squared error of these estimators.