Further results on the trace of a noncentral wishart matrix

In an earlier article Mathai (1980) has given compact representations for the moments and cumulants of the trace of a noncentral Wishart matrix. He has also shown that (trA-ntr;∑)/(2ntri∑²)172. is asymptotically standard normal where A is a noncentral wishart matrix with n degrees of freedom and covariance matrix [0, In the present article explicit expressions for the exact density of the trace are given in terms of confluent hypergeometric functions and in terms of zonal polynomials for the general case and as finite sums when the sample size is odd. As a consequence of some of these representations some summation formulae for zonal polynomials are also given     

Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'

In the estimators t ₃ , t ₄ , t ₅ of Mukerjee, Rao & Vijayan (1987), b _{y x} and b _{y z} are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b _{y x} and b _{y z} in t ₃ , t ₄ , t ₅ , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b _{x z} in t ₅ is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t ₃ , t ₄ , t ₅ , as given in Ahmed (1998 Section 3) are computed assuming that our b _{y x} and b _{y z} are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t ₀ , quoted also in Ahmed (1998), is no better than t ₅ of Mukerjee at al. (1987).     

Time series analysis for repeated surveys

Estimation of a characteristic based on surveys repeated at regular intervals is considered. A state space formulation is given for the problem and the Kalman Filter is used to obtain an estimate and its variance. Some examples are also given to illustrate the methodology.     

The effects of crisis,cynicism about change,and value congruence on perceptions of authentic leadership and attributed charisma in the 2008 presidential election

The current study examines leadership in the context of the 2008 presidential election. Longitudinal data were collected across three regions of the United States to yield 414 responses. Perceptions of crisis were positively related to attributed charisma but not perceptions of authentic leadership. Value congruence moderated the relationship between cynicism and attributed charisma for Obama (but not for McCain) and between cynicism and perceptions of authentic leadership for McCain (but not for Obama). Attributed charisma was found to have augmenting effects over authenticity in predicting voting behavior. The contributions made to the charismatic, authentic, and crisis leadership literatures are discussed and directions for future research presented.     

Assessing mental health and service needs among refugees in Malaysia

Refugees in Malaysia often experience economic insecurity and poverty, poor health, poor mental wellbeing and limited legal rights. Using a survey with quantitative measures and open‐ended questions, we assessed socio‐demographic characteristics, mental health (RHS‐15), and service needs, including interest in group support services, among 86 Dari‐ and Arabic‐speaking refugees living in Kuala Lumpur. High levels of emotional distress were found, as nearly all participants scored positive for distress and average scores were 2.5 times above the cut‐off signifying distress. Distress scores did not vary based on most factors examined, although being married was associated with lower levels of distress. All but one participant expressed interest in participating in a support group. Barriers to potential participation included childcare, sickness and transportation. Additional mental health and social supports are needed among refugees residing in Malaysia. Key Practitioner Message: ? Emotional distress is high among Dari‐ and Arabic‐speaking refugees sampled in Malaysia; ? Participants expressed strong interest in accessing supportive mental health services, including group supports.     

Wife's Education and Urban Family Size in India: The Form of the Relationship

Abstract

The paper examines the net relationship between wife's education and completed family size based on data on 48,5 women, ages 40–49, from one city in India. The results indicate that wife's education has a curvilinear (inverted U) relationship with completed family size. Up to a threshold level of 4.4 years, an increase in wife's education results in larger completed family size; beyond this point it has a depressing effect on family size.     

Measurement of Women's Reproductive Health and Reproductive Rights: An Analysis of Developing Countries

This study attempts to develop measurement scales for women'sreproductive health and reproductive rights by using data from125 developing countries. Data were obtained from varioussources, such as the United Nations and the World Bank. Existing studies on women's reproductive rights suggest atwo-factor model. Women's reproductive health is viewed as beingunidimensional. These proposed attributes are evaluated usingconfirmatory factor analysis. Results indicate the presence oftwo sub-dimensions related to women's reproductive rights. Aone-dimension model of women's reproductive health is empiricallysupported. Validity and reliability of the scales are assessed.Limitations of the measurement scales are discussed.     

Some complex variable transformations and exact power comparisons of two-sided tests of equality of two Hermitian covariance matrices

Power studies of tests of equality of covariance matrices of two p-variate complex normal populations σ₁ = σ₂ against two-sided alternatives have been made based on the following five criteria: (1) Roy's largest root, (2) Hotelling's trace, (4) Wilks' criterion and (5) Roy's largest and smallest roots. Some theorems on transformations and Jacobians in the two-sample complex Gaussian case have been proved in order to obtain a general theorem for establishing the local unbiasedness conditions connecting the two critical values for tests (1)–(5). Extensive unbiased power tabulations have been made for p=2, for various values of n₁, n₂, λ₁ and λ₂ where n₁ is the df of the SP matrix from the ith sample and λ₁ is the ith latent root of σ₁σ^-1₂ (i=1, 2). Equal tail areas approach has also been used further to compute powers of tests (1)–(4) for p=2 for studying the bias and facilitating comparisons with powers in the unbiased case. The inferences have been found similar to those in the real case. (Chu and Pillai, Ann. Inst. Statist. Math. 31.