A generalization of Tyler's M-estimators to the case of incomplete data

Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established until today. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's Mestimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix estimator remains distribution-free under the class of generalized elliptical distributions. Its asymptotic distribution is also derived and a fast algorithm, which works well even for high-dimensional data, is presented. A simulation study with clean and contaminated data covers the complete-data as well as the incomplete-data case, where the missing data are assumed to be MCAR, MAR, and NMAR. --covariance matrix,distribution-free estimation,missing data,robust estimation,shape matrix,sign-based estimator,Tyler's M-estimator

Long-Range Forecasting for a Consumer Durable in an International Market

There has been a substantial amount of interest recently in long-range planning. One necessary component of the long-range plan Is the long-range forecast. In contrast to the emphasis on the planning process, however, little attention has been given to forecasting. This study considers the problem of long-range forecasting in a situation which is of growing importance — forecasting sales for international markets. Many researchers appear to operate under the impression that causal models (i.e., models based on an analysis of underlying factors) lead to more accurate sales forecasts than those provided by naive models (i.e., projections based on historical sales data only). A survey of the research literature led to the conclusion that this confidence in causal models is virtually unsupported. One can hardly criticize firms, then, for relying primarily upon naive models for sales forecasting since these models are simpler and less expensive than causal model. This study was based on the hypothesis that causal models are superior to naive models in certain situations. The key element of^these situations is that -there are large changes. Long-range sales forecasting usually involves such large changes; and there are many reasons to expect that long-range forecasting for international markets is a situation in which substantial changes will occur (e.g., the Kennedy round tariff cuts and the formation of common markets.) A causal model was developed to provide long-range forecasts of the international market for still cameras. This model provided unconditional forecasts of unit camera sales by country for year t + n on the basis of l) knowledge about camera sales in year t and 2) predicted changes in four causal variables from year t to t + n. These four causal variables included, in order of importance, per capita income, price of cameras, number of potential buyers and quality of cameras. The predictive ability of the causal model was superior to that of a naive model purporting to represent current practice. Each model was used to provide backcasts of 195^ camera sales in 17 countries on the basis of data from 1967 to i960 only. The mean absolute percentage error for the causal model was 2% while that for the naive model was h%. This result was statistically significant (0? = .05); but, more importantly, it appeared to have great practical significance. An evaluation, based on very conservative subjective estimates, indicated that such an improvement in accuracy would have a present value worth in excess of one percent of a typical firm\u27s yearly sales volume. Further support for the use of the causal model was obtained by noting that the standard errors of the estimated relationships were low (evidence of reliability), that the estimates of causal relationships from different measurement models were in rather close agreement (evidence of construct validity), and that the causal model performed well in another situation where predictions were provided for I96O-65 camera sales in 11 new countries (evidence of concurrent validity). The causal relationships were initially specified by a subjective analysis. Various parts of the causal model were then updated by use of a number of measurement models including an analysis of differences among sales rates for 30 countries, of differences among changes in the sales rates from 1961 to 1965 for 21 countries, and of differences among six income categories from United States household survey data. This updating led to a modest, though valuable, gain as the mean absolute percentage error of the 195*+ backcast was reduced from 2\u3eQPf0 to the 23$ mentioned above. Additional benefits associated with the development of the causal model included the ability to evaluate large changes in the market; to estimate current sales where trade and production figures are inadequate; to evaluate alternative assumptions about the future rapidly and cheaply; and to identify markets which have not been fully exploited. In summary, the study argues that the development of better long-range forecasting models is an important problem; describes the development of causal models; and demonstrates the superiority of causal models over naive models in a case involving long-range forecasting for international markets

A COMPARISON BETWEEN MOTIVATIONS AND PERSONALITY TRAITS IN RELIGIOUS TOURISTS AND CRUISE SHIP TOURISTS

The purpose of this paper is to analyze the motivations and the personality traits that characterize tourists who choose religious travels versus cruises. Participating in the research were 683 Italian tourists (345 males and 338 females, age range 18–63 years); 483 who went to a pilgrimage travel and 200 who chose a cruise ship in the Mediterranean Sea. Both groups of tourists completed the Travel Motivation Scale and the Big Five Questionnaire. Results show that different motivations and personality traits characterize the different types of tourists and, further, that motivations for traveling are predicted by specific —some similar, other divergent— personality trait

A generalization of Tyler's M-estimators to the case of incomplete data

Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's M-estimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix estimator remains distribution-free under the class of generalized elliptical distributions. Its asymptotic distribution is also derived and a fast algorithm, which works well even for high-dimensional data, is presented. A simulation study with clean and contaminated data covers the complete-data as well as the incomplete-data case, where the missing data are assumed to be MCAR, MAR, and NMAR.

African manufacturing firm : an analysis based on firm surveys in seven countries in sub-Saharan Africa

This book is a comprehensive treatment of the organized (i.e. non-household) manufacturing sector in sub-Saharan Africa. It covers themes such as: the size and distribution of firms in Africa; entrepreneurship, labor and the regulatory business environments in Africa; the dynamic problem of growth and investment of firms. After a short overview (Part I), Part II examines the size distribution of enterprises, production relations in African manufacturing and the relative productivities of small and large firms. Part III provides detailed discussion of the factors of production entrepreneurship, finance, labor, and the regulatory and business environments in which the firms operate

Characteristics of trainee counselors in terms of Eysenck's progressive scientific paradigms, intelligence, personality, & ideology, and success in graduate study

Current gross categorical models of classification for human behavior are unsatisfactory, a science by consensus that is unreliable, invalid, and gives rise to psychological tests that use sophisticated statistics to poorly mirror diagnoses that are already unreliable and without scientific validity. Both for diagnosis and progress in therapy, current diagnostic practices should be replaced by H.J. Eysenck's multifactorial dimensional models. Eysenck's paradigms already rival the scientific complexity and accuracy of the "hard" sciences. The unique and special individual can be measured dimensionally, his/her progress monitored accurately and the current state of the individual and the scientific paradigm shared with each client. Eysenck's paradigms "describe" the individual's typical behavioral repertoire and "explain" the biological determinants of behavior. The evolution of Eysenck's paradigms are developed in great detail and with the aid of many illustrations. Forty-seven trainee counselors of both sexes from two training sites are described in terms of basic biographical data and on Eysenck's progressive scientific paradigms, intelligence, personality and ideoloqy, An attempt was made to determine some linear combination of biographical data and/or trainee characteristics that might predict outcome in the counselor training program. Psychological tests confirmed that trainees had bright/normal to superior intelligence, with humane, stable, extraverted, truthful personalities, and radical, tender-minded and socialistic values and attitudes. A series of two way ANOVAs for site and sex indicated that biographical data and characteristics for trainees were similar but that outcomes differed. Eysenck's progressive scientific paradigms confirm the astute observations of Carl Rogers' and the existential, humanistic and experiential counselor training tradition. A series of canonical correlations were completed with biographical data and trainee characteristics as independent variables and outcome measures for the first term as dependent variables. Overall, there was no meaningful combination of biographical data and/or characteristics of trainees that were related to outcome variables. However, for site and sex characteristics of trainees were differentially related both positively and negatively to outcome. For men, many positive (good) characteristics were strong indicators for negative outcome