We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i)...

Bayesian inference about small areas is of considerable current interest, and simultaneous intervals for the parameters for the areas are needed because these parameters are correlated. This is not usually pursued because with many areas the problem becomes difficult. We describe a method for finding simultaneous credible intervals for a relatively large number of parameters, each corresponding...

Abstract. Let X1, ..., Xn1 be a random sample from a population with mean μ1 and variance σ 2 1 , and Y1, ..., Yn2 be a random sample from another population with mean μ2 and variance σ 2 2 independent of {Xi, 1 ≤ i ≤ n1}. Consider the two sample t-statistic T = X̄−Ȳ −(μ1−μ2) √ s1/n1+s 2 2/n2 . This paper shows that lnP (T ≥ x) ∼ −x2/2 for any x := x(n1, n2) satisfying x → ∞, x = o(n1 + n2) as n...

Rice Husk Ash (RHA) is natural Pozzolan containing reactive silica and/or aluminum. When the material is mixed with lime in powdered form and in the presence of water, it will set and harden like cement. This work uses Osadebe’s optimization model to optimize the shear modulus of concrete made from RHA. The strengths predicted by the model are in good agreement with their corresponding experime...