The latter is an especially attractive characterization of the nth central binomial coefficient. Contrast this with the nth central trinomial coefficient, B(n), defined to be the largest coefficient of the polynomial (1 + x + x). There is no simple closed-form expression for B(n) [2]. It possesses recursion (n+ 1)B(n+ 1) = (2n+ 1)B(n) + 3nB(n− 1), B(0) = B(1) = 1 and asymptotics B(n) ∼ r 3 4π n...

We analyse the role of time-variation in coeffi cients and other sources of uncertainty in exchange rate forecasting regressions. Our techniques incorporate the notion that the relevant set of predictors and their corresponding weights, change over time. We find that predictive models which allow for sudden, rather than smooth, changes in coeffi cients significantly beat the random walk benchma...

The aim of the research is to optimize drilling process parameters while glass fi bre reinforced composites using solid carbide drill by integrating response surface methodology and Taguchi technique. Drilling includes cutting speed, Feed rate point angle with three levels. responses measured against these are; material removal rate, roughness, oversize delamination factor. ANOVA analysis carri...

Modeling of complex systems is commonly confronted with high dimensional set of independent variables. Similarly, econometric models are usually built using time series data that often exhibit nonstationarity due to the impact of some policies and other economic forces. In both cases, linear regression modeling may yield unstable least squares estimates of the regression coeffi cients. Principa...

Quadratic trigamma functions and reciprocal binomial coeffi cients sums are investigated in this paper. Closed form representations and integral expressions are developed for the infinite series.

The Sit-to-Stand test (STST) involves comparing the change in a person’s non-weight-bearing and weightbearing foot posture to quickly classify a person’s overall foot mobility. Despite the simplicity of the test, its reliability and validity has not been established. The purpose of this study is to determine the intra-rater and inter-rater reliability of the STST as well as its validity. Ninety...

Appendix B.1 extends the results in Section 4 on the identification of average exogenous random coeffi cients to study a panel structure and proxies included in the Y equation. Appendix B.2 characterizes the OVB of nonparametric regression and IV methods when U enters the Y and W equations additively separably. Appendix B.3 characterizes the nonparametric regression bias for β̄(x, x∗|x∗, s) and ...