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Effects of resistance and aerobic training on the ease of physical activity during and after weight loss are unknown. The purpose of the study was to determine what effect weight loss combined with either aerobic or resistance training has on the ease of locomotion (net V[Combining Dot Above]O2 and heart rate). It is hypothesized that exercise training will result in an increased ease, lowers heart rate during locomotion. Seventy-three overweight premenopausal women were assigned to diet and aerobic training, diet and resistance training, or diet only. Subjects were evaluated while overweight, after diet-induced weight loss (average, 12.5 kg loss), and 1 year after weight loss (5.5 kg regain). Submaximal walking, grade walking, stair climbing, and bike oxygen uptake and heart rate were measured at all time points. Weight loss diet was 800 kcal per day. Exercisers trained 3 times per week during weight loss and 2 times per week during 1-year follow-up. Resistance training increased strength, and aerobic training increased maximum oxygen uptake. Net submaximal oxygen uptake was not affected by weight loss or exercise training. However, heart rate during walking, stair climbing, and bicycling was reduced after weight loss. No significant differences in reduction in heart rate were observed among the 3 treatment groups for locomotion after weight loss. However, during 1-year follow-up, exercise training resulted in maintenance of lower submaximal heart rate, whereas nonexercisers increased heart rate during locomotion. Results suggest that moderately intense exercise is helpful in improving the ease of movement after weight loss. Exercise training may be helpful in increasing the participation in free-living physical activity.

In vitro and animal model studies have indicated that oxidative stress from exposure to excess glucose and fatty acids impairs insulin signaling. However, few clinical studies have examined the association between oxidative stress and insulin action, particularly in non-diabetic individuals. The objective of this study was to examine the association between insulin sensitivity and protein carbonyls, a systemic marker of oxidative stress, in healthy individuals, and to determine if the magnitude of the relationship differed in African Americans (AA), who are at elevated risk for type 2 diabetes, relative to European Americans (EA). Subjects were 53 normal-glucose-tolerant women (25 AA, mean BMI 28.4 ± 6.2, range BMI???; mean age 33.1 ± 13.5, range age????; 28 EA mean BMI 26.2 ± 5.9, range BMI???; mean age 31.6 ± 12.4, range age??? ) . Insulin sensitivity was determined using an intravenous glucose tolerance test incorporating [6,6-2H2]-glucose, and a two-compartment mathematical model. Multiple linear regression results indicated that insulin sensitivity was independently positively associated with protein carbonyls in AA (r = 0.33, P

Elevated serum high-sensitivity C-reactive protein (hs-CRP) and low serum 25-hydroxyvitamin D [25(OH)D] are associated with increased cardiovascular disease (CVD) risk. Ethnic differences in serum hs-CRP and 25(OH)D concentrations and CVD are known. Objectives: to investigate the ethnic differences in hs-CRP concentrations, to assess the influence of 25(OH)D on these ethnic differences and to examine the influence of 25(OH)D on association between hs-CRP and cardiovascular health indices. Subjects: 62 healthy adults [26 African Americans (AA), 26 European Americans (EA), and 10 Hispanic Americans (HA)], ages 18–55 years. Serum hs-CRP and 25(OH)D as well as pulse wave velocity (PWV), augmentation index (AIx), and flow-mediated dilatation (FMD) were measured. hs-CRP was inversely associated with 25(OH)D (r=−0.25,P=0.049), and hs-CRP was positively associated with PWV (r=0.29,P=0.04). The association of hs-CRP with PWV attenuated after adjustment for 25(OH)D (P=0.15). hs-CRP was higher in AA compared to EA (P=0.05); this differences was reduced by 32% after adjusting for serum 25(OH)D. Conclusion: eventhough the inverse association between serum 25(OH)D and CRP does not infer causality, lower serum 25(OH)D may increase risk for inflammation and endothelial dysfunction. The lower 25(OH)D in AA may predispose to greater inflammation and associated vascular dysfunction.

Two recent examinations reported a strong association between blood pressure (BP) and resting energy expenditure (REE), independent of body mass and body composition. Both reports postulate that neurohumoral processes that contribute to variation in REE may partly mediate the body mass effect on BP. Therefore, we examined the relationship of REE and BP in 108 asymptomatic women (a) to confirm previous findings in a novel population and (b) to examine the impact of a marker of sympathetic tone on this relationship, as this was indicated as a potentially salient intermediary in previous reports. All testing was performed during a 4-day admission to the General Clinical Research Center. Resting energy expenditure was measured by indirect calorimetry, body composition was determined by dual-energy x-ray absorptiometry, and 24-hour fractionated urinary norepinephrine was determined by high-performance liquid chromatography. Multiple linear regression revealed REE as a significant predictor of systolic BP (β = 0.30, P = .04), independent of race (β = 0. 28, P = .01), age (β = −0.02, P = .80), height (β = −0.38, P = .08), fat mass (β = 0.22, P = .20), fat-free mass (β = 0.08, P = .65), and 24-hour fractionated urinary norepinephrine (β = 0.06, P = .57); and the same model using diastolic BP as the dependent variable approached significance (β = 0.24, P = .09). This study affirms previous findings that REE may be a potential mediator in resting BP, independent of many well-cited factors and, additionally, a marker of sympathetic tone.

We have previously shown that Achilles tendon length is related to walking economy on the flat, presumably because of increased stretch-shortening cycle elastic energy savings. In addition, greater walking economy in African American (AA) women compared to European American (EA) women is explained by longer Achilles tendons in AA women. The purposes of this study were to determine whether economy while walking up a grade and during isometric plantar flexion, two tasks expected to produce proportionately less energy savings from elastic savings are different between AA and EA women. We evaluated walking economy at 4.8 km/h at 0 and 2.5% grade in 48 AA and 48 EA premenopausal women. Plantar flexor muscle metabolic economy (force/ATP) was also evaluated using (31) phosphate magnetic resonance spectroscopy ((31)P-MRS). AA women walked on the flat more economically (net VO(2), AA 8.3 and EA 8.9 ml kg(-1) min(-1), P = 0.04). No significant ethnic differences were observed while walking up a 2.5% grade or in (31)P-MRS determined plantar flexor muscle metabolic economy. These data support our previous study's suggestion that AA women are more economical while walking on the flat. On the other hand, in activities in which stretch-shortening cycle elastic energy savings would be expected to be reduced (grade walking and isometric force production), no differences in economy during grade walking or isometric force production were observed suggesting that biomechanical, i.e. stretch-shortening cycle elastic energy savings differences rather biochemical differences contribute to the better flat walking economy observed in AA women.

Purpose To compare the effects of six weeks of high intensity interval training (HIIT) vs continuous moderate intensity training (MIT) for improving body composition, insulin sensitivity (SI), blood pressure, blood lipids, and cardiovascular fitness in a cohort of sedentary overweight or obese young men. We hypothesized that HIIT would result in similar improvements in body composition, cardiovascular fitness, blood lipids, and SI as compared to the MIT group, despite requiring only one hour of activity per week compared to five hours per week for the MIT group. Methods 28 sedentary overweight or obese men (age, 20 ± 1.5 years, body mass index 29.5 ± 3.3 kg/m2) participated in a six week exercise treatment. Participants were randomly assigned to HIIT or MIT and evaluated at baseline and post-training. DXA was used to assess body composition, graded treadmill exercise test to measure cardiovascular fitness, oral glucose tolerance to measure SI, nuclear magnetic resonance spectroscopy to assess lipoprotein particles, and automatic auscultation to measure blood pressure. Results A greater improvement in VO2peak was observed in MIT compared to HIIT (11.1% vs 2.83%, P = 0.0185) in the complete-case analysis. No differences were seen in the intention to treat analysis, and no other group differences were observed. Both exercise conditions were associated with temporal improvements in % body fat, total cholesterol, medium VLDL, medium HDL, triglycerides, SI, and VO2peak (P < 0.05). Conclusion Participation in HIIT or MIT exercise training displayed: 1) improved SI, 2) reduced blood lipids, 3) decreased % body fat, and 4) improved cardiovascular fitness. While both exercise groups led to similar improvements for most cardiometabolic risk factors assessed, MIT led to a greater improvement in overall cardiovascular fitness. Overall, these observations suggest that a relatively short duration of either HIIT or MIT training may improve cardiometabolic risk factors in previously sedentary overweight or obese young men, with no clear advantage between these two specific regimes (Clinical Trial Registry number NCT01935323). Trial Registration ClinicalTrials.gov NCT01935323

OBJECTIVES: To assess the effectiveness of a men's 'waist loss' program over one year in Indigenous men. DESIGN: Pre- and post-test measurements of 47 Indigenous men on four island groups in the Torres Strait region of Northern Australia involved in a version of the 'GutBuster' program, modified by and for Indigenous men. RESULTS: Weight, waist and hip size of 47 men, and body fat estimated from electrical impedence measures of 27 men, were compared at baseline, after approx 2 months, approx 6 months and approx one year. Average weight loss was 3.3 kg (3.5%), and waist loss 4.0 cm (3.5%). The average percentage decrease in fat mass (FM) was 10.8%. An environmental audit technique highlighted modifications needed to the environment to assist behaviour change. CONCLUSIONS: Education-behaviour change interventions of this kind may offer opportunities for health improvements in Indigenous men.

In 1907 Hans Hahn of Vienna published an article on non-archimedean systems of quantities [1]. The study of such systems, according to Hahn, goes back to Paul du Bois-Reymond and Otto Stolz. (It actually goes back further — consider horn angles in ancient Greece, for example.) The work of du Bois-Reymond was published between 1870 and 1882 (Hahn cites only two articles, 1875 and 1877). That of Stolz appeared from 1879 to 1896 (Hahn cites articles of 1881, 1883 and 1891). Hahn also observes that Rodolfo Bettazzi handles some questions of this kind in his Teoria delle grandezze of 1890 [2], and that Giuseppe Veronese built a geometry without use of the Archimedean axiom in his “mathematically and philosophically significant” Fondamenti di geometria of 1891, which was translated into German by Adolf Schepp with some changes by Veronese in 1894 [3, 4]. Veronese subsequently answered various objections to his work — Hahn cites articles of 1896, 1897 and 1898. Tullio Levi-Civita, as Hahn says, gave an arithmetical representation of Veronese’s continuum in 1892/1893 and 1898 [5, 6]. Finally, Hahn cites Arthur Schoenflies’ article of 1906 [7].

Tests for stochastic dominance are important tools for the comparison of distributions between pairs of random variables. In finance, dominance criteria can potentially provide an unambiguous ranking of the desirability of different assets while placing only general restrictions on the preferences of investors. In welfare economics, dominance concepts allow for the ranking of income distributions using generally accepted welfare criteria. Existing dominance test procedures suffer from a number of weaknesses. One weakness concerns restrictions on the class of distribution functions that may be used as a basis for testing. While early literature in this area typically ignored sampling errors, this issue has been addressed in more recent literature, but only at the cost of restricting the class of parametric distributions discussed; see e.g. Stein and Pfaffenberger (1986). Since dominance criteria are attractive primarily because they allow for a ranking of returns on risky assets or income distributions, while placing only weak restrictions on preferences, it is important that dominance tests retain a degree of generality, and hence remain nonparametric in nature. Another weakness of existing dominance tests is that these often specify the null hypothesis improperly; see e.g. Bishop et al. (1989). For example, most test procedures make use of the null hypothesis that two distribution or quantile functions are identical. The hypothesis of dominance may be viewed as an hypothesis of inequality in a particular direction between two distribution or quantile functions. If such an hypothesis is rejected, then dominance cannot be sustained, a result that may or may not be caused by the equality of the two distribution or quantile functions. On the other hand, if the null hypothesis of equality is rejected, then the two distributions cannot be said to be equal, but the cause may or may not be that one dominates the other. Thus the null hypothesis of equality is not very helpful in providing information about dominance; see Levy (1992, p. 574).

The theory of least squares is taken to encompass any estimation procedure, algorithm or iterative scheme whose solution is obtained either by minimizing the square of a selected euclidean length, or equivalently, by requiring conformity to the corresponding orthogonality condition. Viewed in this way, least squares may accommodate not only those methods that bear its name, but also generalized instrumental variables estimation (GIVE), the generalized method of moments (GMM), generalized minimum chi-square estimation sometimes referred to as summary generalized least squares (Cragg 1993), and certain problems in robust estimation and restricted maximum-likelihood estimation, under the broad heading of iterated re-weighted least squares (IRLS); see e.g. Green (1984). In this broad context, the first aim of this paper is to synthesize various different methods of econometrics in terms of three characterizations of least squares. A second aim is to illustrate these characterizations with examples, paying particular attention to applications of IRLS to restricted maximumlikelihood estimation in econometrics. A third aim is to stress the importance of the freedom equation approach to restricted estimation and to provide a proof that restricted estimation is never less efficient than unrestricted estimation. Proofs of the efficiency of restricted estimation are standard for linear models in econometrics, but no proofs are available of a more general kind. The principal vehicle of discussion is co-ordinate-free multivariate analysis, by which is meant that form in which the basic elements (e.g. variables) and the derived elements (e.g. estimators) may be treated as points in vector spaces without explicit bases. The analysis may then be described geometrically and can often usefully be illustrated diagrammatically.

This paper is concerned with the general problem of testing one form of covariance structure against another in a normal linear regression. It is shown that all the point-optimal tests recently proposed by King and his associates can be interpreted as special cases of a Cox test for non-nested hypotheses. This provides a synthesis of a whole range of point-optimal tests as well as demonstrating that King and his associates have exposed a class of Cox tests which have an exact distribution.

The writer contends that the mini‐computer provides a very substantial potential area of application for the processing of information, management control and physical control of warehouse plant. Mini‐computers can be coupled with a whole range of peripheral input/output devices, from which can be developed configurations extending from very simple systems costing as little as £3,500.

Several recently proposed tests for separate regressions in econometrics are re-examined in the light of recommendations by Cox (1961). This re-examination points to simplified criteria and emphasizes the unity underlying the tests. The exact distributions of some of the tests are developed under the tested hypothesis. These are given a geometrical characterization which is helpful in exploring relations with the classical F -test. An orthogonal decomposition is proposed which provides a direct link between the F -test and tests based upon artificial nesting.

This paper attempts to synthesize various procedures for testing non-nested hypotheses within the framework of artificial nesting, and establishes the result that different tests correspond to different treatments of its identification problem. Numerical and a priori identification methods are distinguished. We derive two modified likelihood ratio tests that are asymptotically equivalent to the Cox-test and explain the relationship between them. The tests are consistent.(This abstract was borrowed from another version of this item.)

When coefficients of endogenous variables are known, it is demonstrated that two-stage least squares and instrumental variable estimators are invariant to the form in which these variables enter computations, as raw data or estimates. Exclusion of instruments and knowledge of coefficients are related to identifiability testing, and a test presented.

Within the framework of linear regression, errors arising from artificial inclusion or exclusion of variables are considered with augmentations or restrictions on a given maintained hypothesis. This permits exploitation of relations between tests based on Wald and Lagrange Multiplier Principles. It is demonstrated that the standard F test, though based on biased estimators, is nevertheless valid. The traditional analysis of misspecification is applied to the linear specialization of tests for separate families of hypotheses. An empirical example is provided examining the effect of labour legislation on the growth of Canadian trade union membership, using annual data for 1925-72.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

This note is concerned with discrimination and significance testing in respect of non-nested hypotheses in econometrics. It is argued that logic requires a test of discrimination to be one-tailed and a significance test for a non-nested hypothesis to be two-tailed. It is also argued that the significance test of a pair of non-nested hypotheses sensibly involves consideration of another. This is introduced so that the cause of deviation from the tested hypothesis away from the alternative may be attributed to it.

The mixed fortunes of Paul du Bois-Reymond's infinitary calculus and ideal boundary between convergence and divergence are traced from 1870 to 1914. Cantor, Dedekind, Peano, Russell, Pringsheim and others objected. Stolz, Borel, Hardy and others accepted, at least in part, and built further. Hausdorff to some extent effected a compromise. The differing attitudes of the different participants toward infinitesimals and infinitely large quantities are described. In addition to shedding some light on the status of infinites, the whole story serves as a study of mathematical change, and shows that the “proof-refutation” process described by Lakatos is only one aspect of mathematical development. The story also sheds some light on the rise of 20th century functional analysis, algebra and topology.

summary This paper discusses the traditional specification problem from a geometric (or co-ordinate-free) viewpoint. While the traditional emphasis is on the properties of estimators, the geometric approach also allows an easy development of corresponding results for inference. Errors arising from artificial inclusion or exclusion of variables are considered in terms of augmentations or restrictions on a given maintained hypothesis, and this allows a corresponding interpretation of tests based upon the Wald and Lagrange Multiplier Principles. It is demonstrated that biases arising from incorrect exclusion of variables do not invalidate the traditional F-test.

Summary In econometrics it is common for variables to be related together in a set of linear, multilateral and causal interdependencies. This type of system generally has properties which are unsatisfactory for application of classical regression techniques. Consequently, alternative estimation methods have been developed. This paper explores the relations between several such methods in terms of symmetric idempotents of predetermined variables and their orthogonal complements. Generalizations of two‐ and three‐stage least squares and instrumental variables are considered, including Wicken's estimator.2 The relative efficiencies of the estimators are also discussed. ∗ Some of the ideas in this paper appeared in Reference 1(a), a later version of which was presented to the World Congress of the Econometric Society, Rome, 1965.1(b) Since these papers appeared, the mathematical exposition has been improved, the results made more general and some new results (on efficiency) added. Some of the results reported...

We consider Cauchy's use of the infinitely small in his textbooks. He never examined fully his concept of variables with limit zero, and he sometimes argued as if he were using actual infinitesimals. Occasionally he adopted an epsilon-delta approach. The author argues that historical evaluations of mathematical analysis may and should be made in the light of both standard and non-standard analysis. From this point of view, Cauchy's move toward founding analysis entirely on the standard real number system does not seem to have been inevitable. Some historical observations by the founder of non-standard analysis, Abraham Robinson, are extended, and in one case contested. It is shown that some of Cauchy's alleged errors are explained if he is admitted to have been thinking of actual infinitesimals and infinitely large integers. Cauchy's definitions of differential in his textbooks are examined, and the author shows that the earlier of his two definitions of total differential works well, but the later does not.

Cet article développe une condition d’invariance du modèle de régression à coefficients aléatoires (RCA) et de cette façon permet : (i) d’étendre les résultats de Rao (1963, 1967)”; (ii) de fournir une nouvelle démonstration de l’égalité des estimateurs des moindres carrés généralisés directs et ceux en deux étapes du modèle RCA”; et (iii) de rectifier une proposition de McAleer (1992) pour les modèles mixtes., This paper develops an invariance condition for the random coefficients regression (RCR) model and thereby: (i) exends the results originally proposed by Rao (1965, 1967); (ii) provides a new proof of the equality of the direct and two-step estimators of the RCR model; and (iii) corrects a result claimed in McAleer (1992) for mixed models.

T HE purpose of this paper is to extend the traditional analysis of specification error to models that are separate (i.e., non-nested), in the sense that one may not be obtained from the other by the imposition of restrictions or as a limiting form of a suitable approximation. The general theoretical approach to testing separate families of hypotheses was pioneered by Cox (1961, 1962), and subsequent work has largely been based on the many suggestions in these two papers. In an important extension, Atkinson (1970) derived a test statistic that is asymptotically equivalent to the Cox test under the null hypothesis. However, Pereira (1977) showed that while the Cox procedure always provides a consistent test of the null, Atkinson's variation does not. This is an important result since the power of an inconsistent test does not tend to unity in large samples, where power is taken to be the probability of rejecting a false null model. The general results obtained by Cox for separate distributions were specialized to regression analysis by Pesaran (1974) and Pesaran and Deaton (1978). Dastoor (1981a) and Fisher and McAleer (1981) modified the Cox test using Atkinson's procedure and demonstrated Pereira's caveat regarding test inconsistency to be unwarranted for separate linear and non-linear regressions, respectively, with normal disturbances. Several algorithms for calculating approximations to the Cox statistic via artificial regression models have recently been developed by Davidson and MacKinnon (1981), and Fisher and McAleer (1981). These test statistics, which are asymptotically equivalent under the null as well as under local alternatives (see Pesaran, 1982b), will also be analyzed with regard to the effects of misspecification. In spite of the potential usefulness of the Cox test in applied econometric research, it is surprising that there have been so few published empirical papers employing it (Quandt, 1974; Deaton, 1978). It is also notable that theoretical work involving considerations of power has concentrated on local, I rather than fixed, alternatives. Since serious misspecification arises only when the difference between the null and the alternative model does not disappear in large samples, it would seem more helpful from the practical viewpoint to analyze specification error when the null is tested against a fixed alternative, and this is one of the primary objectives of the present paper. The other objective is to provide an empirical example illustrating the consequences of misspecifying separate models. The plan of the paper is as follows. Alternative procedures for testing separate regression models are outlined in section II, and the consistency of the tests is investigated in the light of specification error in section III. It is demonstrated that (i) both the Cox and Atkinson procedures provide consistent tests of the null when variables are incorrectly included in the alternative; and (ii) it is possible that neither procedure will provide a consistent test when variables are incorrectly excluded from the alternative. It is argued that specification error in the null does not affect the consistency of the tests. Some consequences of the results are discussed in section IV. An illustrative empirical example related to alternative specifications of the U.S. long-run demand for money function is presented in section V. Some concluding remarks are given in section VI. Received for publication May 18, 1981. Revision accepted for publication February 25, 1982. * Australian National University, Queen's University, and Australian National University, respectively. The authors wish to thank Noxy Dastoor, Adrian Pagan, Deane Terrell, and especially Anil Bera, for helpful comments, Les Godfrey for permission to refer to his unpublished paper, and Eva Klug for efficient research assistance. Responsibility for the final product rests with the authors alone. The present paper is a substantially revised and extended version of McAleer and Fisher (1981). I When the concept of local alternatives is used, the sample size is taken to be "sufficiently large" so that the asymptotic results are valid, but not so large that the sequence of local alternatives has converged to the null (see Cox, 1962, p. 407). Pesaran (1982a) examines the local power of alternative tests of non-nested models, but makes the somewhat restrictive assumption that the dimension of the null model is not exceeded by that of the alternative.

This paper demonstrates that the extended linear expenditure system with durables (DELES) satisfies first-order conditions for local unidentifiability, and discuss alternative methods that might be used to achieve identifiability, as well as their implications. Estimates are presented using seasonally adjusted, quarterly Australian data from 1959Q4 to 1976Q2. This exercise compares the effects of allowing for first-order autocorrelation. We fix the decay rate for durables to secure identifiability, however, the estimates of the remaining parameters are insensitive to the value chosen. This suggests a major difficulty in interpreting DELES and leads us to reconsider its limiting properties. (This abstract was borrowed from another version of this item.)