Multiple comparisons of mean vectors with large dimension under general conditions

ABSTRACT

Multiple comparisons for two or more mean vectors are considered when the dimension of the vectors may exceed the sample size, the design may be unbalanced, populations need not be normal, and the true covariance matrices may be unequal. Pairwise comparisons, including comparisons with a control, and their linear combinations are considered. Under fairly general conditions, the asymptotic multivariate distribution of the vector of test statistics is derived whose quantiles can be used in multiple testing. Simulations are used to show the accuracy of the tests. Real data applications are also demonstrated.     

A study of subjective visual disturbances in jewellery manufacturing

Subjective Visual Disturbances are silent adversaries that appear over a period of continued exposure and arise when the visual demands of the tasks exceed the visual abilities of the user. Jewellery manufacturing activity involves precision designs, setting the metal and stones, polishing and filing which requires higher visual demand. Therefore, it is expected that the jewellery manufacturing workers may experience subjective visual disturbances. This study was taken up with the following objectives 1) To study the presence of subjective visual disturbances among jewellery manufacturing workers and compare the same with VDT operators 2) To study the effect of work exposures on subjective visual disturbances and 3) to ascertain whether subjective visual disturbances have any permanent vision related problems. The study was carried out on jewellery manufacturing workers, VDT operators and on graduate students. The symptoms of subjective visual disturbances were identified using a questionnaire developed by Sheedy (2003). Viewing distances were measured and visual angles were calculated. The eye check--ups were also carried out. The subjective visual disturbances were higher in jewellery manufacturing workers. The findings suggest that work exposure has an impact on the causation of subjective visual disturbances. No pathological conditions of the eyes were observed.     

Social Health Indicators and Economic Growth: Evidence from East Asia and Pacific,Middle East and North Africa,South Asia,and Sub-Saharan Africa

The objective of this study is to empirically investigate a two-way statistical relationship between the social health indicators and economic growth in the context of four major regions of the world i.e., East Asia and Pacific, Middle East and North Africa (MENA), South Asia and Sub-Saharan Africa. To recognize the relationship between the two variables, a time series, co-integration and Granger causality tests have been employed. Aggregate secondary data pertaining to these four regions from 1975 to 2011 on economic growth and social health indicators i.e., infant mortality, child abuse, child poverty, unemployment, weekly wages, health insurance coverage, teenage suicide, teenage drug abuse, high school dropouts, poverty, out-of-pocket health costs, homicides, alcohol related traffic fatalities, food insecurity, income inequality, HIV/AIDS, tuberculosis, basic health units and rural health centers has been used for analysis. This study evaluates four alternative but equally plausible hypotheses, each with different policy implications. These are: (1) social health indicators Granger cause economic growth, (2) economic growth Granger cause social health indicators (the conventional view), (3) There is a bi-directional causality between the two variables and (4) Both variables are causality independent (although highly correlated). The empirical results only moderately support the conventional view that economic growth has significant long run casual effect on social health indicators in East Asia and Pacific, MENA, South Asia and Sub-Saharan Africa. The present study find evident of unidirectional causality running towards economic growth to social health indicators, although, there are some bidirectional causality also exists between the variables. The percentage of unidirectional causality between economic growth and social health indicators is larger than bidirectional or neutrality hypothesis.     

Tests for high-dimensional covariance matrices using the theory of U-statistics

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p?n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.     

Young Children's Evaluations of the Ingroup and of Outgroups: A Multi-National Study

In investigating intergroup attitudes, previous research in developmental psychology has frequently confounded ingroup favouritism and outgroup derogation. The present study, using unconfounded measures, examines the possibility that ingroup favouritism and outgroup derogation are distinct phenomena. Six‐year‐old children (n=594) from five, culturally diverse nations were asked to make various evaluations of the national ingroup and of four national outgroups. The data indicate that although there is overwhelming evidence that young children favour the ingroup over other groups, outgroup derogation is limited in extent and appears to reproduce attitudes held by adult members of the particular nations investigated.     

Study on lumbar kinematics and the risk of low back disorder in female university students by using shoes of different heel heights

The study was taken up to investigate the effects of heel heights on lumbar kinematics and the risk of Low Back Disorder (LBD) in females. Nineteen female university students (24.5 ± 3.36 yrs) volunteered in the study. Lumbar kinematics was measured by using Industrial Lumbar Motion Monitor (iLMM). The volunteers were asked to walk for a distance of 50 meters in 3 different given conditions i.e bare foot (Heel 0), with flat heels (Heel 1) and with high heels (Heel 2). Heights of Heel 1 and Heel 2 were 1.5 ± 0.84 cm and 5.5 ± 1.70 cm respectively. The Lumbar kinematic parameters studied were- Average Twisting Velocity (ATV), Maximum Sagital Flexion (MSF) and Maximum Lateral Velocity (MLV). It was observed that all the above mentioned Lumbar kinematics - ATV, MSF and MLV increases with increase of heel heights, which in turn increases the risk of LBD. As a result of increase in Lumbar kinematic values with increase in heel heights, LBD risk has also increased. Mean and SD of the LBD risk with Heel 0, Heel 1 and Heel 2 were 16.79 ± 6.04%, 19.00 ± 7.38% and 22.11 ± 6.98% respectively. Lower stature with high heels showed higher risk of LBD than the higher stature with high heels.     

Location‐invariant Multi‐sample U‐tests for Covariance Matrices with Large Dimension

For two or more multivariate distributions with common covariance matrix, test statistics for certain special structures of the common covariance matrix are presented when the dimension of the multivariate vectors may exceed the number of such vectors. The test statistics are constructed as functions of location‐invariant estimators defined as U‐statistics, and the corresponding asymptotic theory is used to derive the limiting distributions of the proposed tests. The properties of the test statistics are established under mild and practical assumptions, and the same are numerically demonstrated using simulation results with small or moderate sample sizes and large dimensions.     

Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality

A test for homogeneity of g ? 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n_i, i = 1, …, g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n_i, p → ∞. Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.     

A unified approach to testing mean vectors with large dimensions

AStA Advances in Statistical Analysis - A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance...