Based on a random sample from a population with (unknown) probability density f, this note exhibits a class of statistics f(p) for each fixed integer p [greater, double equals] 0. It is shown that f(p) are uniformly strongly consistent estimators of f(p), the pth order derivative of f, if and...

For the estimation of the mean [mu] of a normal population with unknown variance [sigma]2, Searles (1964) provides the minimum mean squared (MMSE) estimator (1 + [sigma]2/(n[mu]2))-1 in the class of all estimators of the type . This MMSE estimator however is not computable in practice if...

On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a [sigma]-finite measure dominated by the Lebesgue measure on Rm, P = (p1,...,pm), pj = 0, fixed integers, and for x =...

Let Xj = (X1j ,..., Xpj), j = 1,..., n be n independent random vectors. For x = (x1 ,..., xp) in Rp and for [alpha] in [0, 1], let Fj(x) = [alpha]I(X1j < x1 ,..., Xpj < xp) + (1 - [alpha]) I(X1j <= x1 ,..., Xpj <= xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, [alpha] max1 <= N <= n [Sigma]0n(Fj(x) - Fj(x)). It is shown that P[Dn >= L] < 4pL exp{-2(L2n-1 - 1)} for each positive integer n and for all L2 >= n; and, as n --> [infinity], Dn = 0((nlogn)1/2) with probability one.

Madhya Pradesh is a state located in the central part of India, and grows 73% of soybean produced in India. In five villages located in various agro climatic regions of the state, 275 farmers cultivated soybean during 1997-1999, of which 239 farms had practiced rainfed cultivation. A total of...

Biogas is said to be a clean and renewable form of energy. It can replace fossil fuel, thereby eliminating environmental concerns caused by them. Due to several constraints in the process of anaerobic digestion, the potential of this technology is not fully utilized. This paper reviews various...