The six weeks of group tai chi followed by another six weeks of home tai chi training showed significant improvements in mean overall knee pain (P = 0.0078), maximum knee pain (P = 0.0035) and the WOMAC subscales of physical function (P = 0.0075) and stiffness (P = 0.0206) compared to the baseline. No significant change of any outcome measure was noted in the attention control group throughout the study. The tai chi group reported lower overall pain and better WOMAC physical function than the attention control group at weeks 9 and 12. All improvements disappeared after detraining.

This feasibility study compared the effects of Tai Chi (TC) and resistance training (RT) on bone metabolism in the elderly. Twenty eight sedentary, elder adults, were randomized into either TC (n = 14, 78.8 +/-1.3 years) or RT (n = 14, 79.4 +/-2.2 years) to participate in 40 min of exercise per session, 3 sessions/week for 24 weeks. The outcome measures assessed were the concentrations of serum bone-specific alkaline phosphatase (BAP), pyridinoline (PYD), parathyroid hormone (PTH) and calcium, and urinary calcium. The TC group had a higher compliance rate than the RT group. After 6 weeks, (i) both TC and RT resulted in higher level of serum BAP relative to the baseline and the TC group exhibited a greater increase in serum BAP than the RT group; (ii) there was an increase of serum PYD in the RT group only, not in the TC group; and (iii) the BAP/PYD ratio was higher than baseline only in the TC group, and the increase of the ratio in the TC group was greater than that in the RT group. After 12 weeks, the increase in serum PTH in the TC group was higher than the RT group. After 24 weeks, there was a reduction of the urinary calcium level in the TC group relative to the baseline. In conclusion, these findings support that TC is beneficial for increasing bone formation in elderly, and long-term application is needed to substantiate the effect of TC as an alternative exercise in promotion of bone health.

We prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model with knots placed at all observed time points (except the first and last) and uncorrelated residuals. This equivalence then furnishes a rich variety of existing data-driven parameter estimation methods, particularly restricted maximum likelihood (REML) and generalized cross-validation (GCV). This has profound implications for users of HPF who have hitherto typically relied on subjective choice, rather than estimation, for the smoothing parameter. By viewing estimates as roots of an appropriate quadratic estimating equation, we also present a new approach for constructing confidence intervals for the smoothing parameter. The method is akin to a parametric bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and provides a fast and accurate alternative to exact methods, when they exist, e.g. REML. More importantly, it is also the only computationally feasible method when no other methods, exact or otherwise, exist, e.g. GCV. The methodology is demonstrated on the Gross National Product (GNP) series originally analyzed by Hodrick and Prescott (1997). With proper attention paid to residual correlation structure, we show that REML-based estimation delivers an appropriate smooth for both the GNP series and its returns.

In this paper tests are derived for testing neighborhood hypotheses for the one-and multi-sample problem for functional data. Our methodology is used to generalize testing in projective shape analysis, which has traditionally involving data consisting of finite number of points, to the functional case. The one-sample test is applied to the problem of scene identification, in the context of the projective shape of a planar curve.

Computational expressions for the exact CDF of Roy's test statistic in MANOVA and the largest eigenvalue of a Wishart matrix are derived based upon their Pfaffian representations given in Gupta and Richards (SIAM J. Math. Anal. 16:852-858, 1985). These expressions allow computations to proceed until a prespecified degree of accuracy is achieved. For both distributions, convergence acceleration methods are used to compute CDF values which achieve reasonably fast run times for dimensions up to 50 and error degrees of freedom as large as 100. Software that implements these computations is described and has been made available on the Web.