This paper considers multivariate extension of smooth estimator of the distribution and density function based on Bernstein polynomials studied in Babu et al. [2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. J. Statist. Plann. Inference 105, 377–392]. Multivariate version of Bernstein polynomials for approximating a bounded and continuous...

Objective: There are major differences in neonatal and obstetrics outcomes of labour among different ethnicities. The present study compared the neonatal and obstetrics outcomes of labour between the Iranian and Afghan ethnicities. Methods: Neonatal and obstetrics problems were evaluated in Iranian and Afghan pregnant women, who had referred to Ar...

Background and purpose: Research studies indicate that almost 80% of the present day drugs are derived directly or indirectly from medicinal plants. The estimation of a safe starting dose is a concern when a new substance is to be investigated including medicinal plants, in clinical and laboratory studies. This study was intended to explore a simple and reliable method of calcu...

We present new conditions for the strong consistency and asymptotic normality of the least squares estimator in nonlinear stochastic models when the design variables vary in a finite set. The application to self-tuning optimisation is considered, with a simple adaptive strategy that guarantees simultaneously the convergence to the optimum and the strong consistency of the estimates of the model...

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the a...

This article concerns maximum likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain. We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of t...

Let p be a prime k|p−1, t = (p−1)/k and γ(k, p) be the minimal value of s such that every number is a sum of s k-th powers (mod p). We prove Heilbronn’s conjecture that γ(k, p) k1/2 for t > 2. More generally we show that for any positive integer q, γ(k, p) ≤ C(q)k1/q for φ(t) ≥ q. A comparable lower bound is also given. We also establish exact values for γ(k, p) when φ(t) = 2. For instance, whe...

Although the basic building blocks for working with strong encryption have become fairly widespread in the last few years, experience has shown that implementers frequently misuse them in a manner that voids their security properties. At least some of the blame lies with the tools themselves, which often make it unnecessarily easy to get things wrong. Just as no chainsaw manufacturer would thin...