We obtain, for T ε ≤ U = U(T ) ≤ T 1/2−ε, asymptotic formulas for Z 2T T (E(t+ U)− E(t)) dt, Z 2T T (∆(t+ U)−∆(t)) dt, where ∆(x) is the error term in the classical divisor problem, and E(T ) is the error term in the mean square formula for |ζ( 1 2 + it)|. Upper bounds of the form Oε(T 1+εU2) for the above integrals with biquadrates instead of square are shown to hold for T 3/8 ≤ U = U(T ) ≪ T ...

Introduction. People living in rural areas may face specific barriers to finding useful health-related information, and their use of information may differ from their urban counterparts. Method. This random-digit dial telephone survey of 253 people (75% female) living in a rural, medically under-serviced area of Ontario, Canada, follows-up a previous interview study to examine with a larger sam...

In the present article, a new nonparametric estimator of quantile density function is defined and its asymptotic properties are studied. The comparison of the proposed estimator has been made with estimators given by Jones (1992), graphically and in terms of mean square errors for the uncensored and censored case.

Motivated by estimation problems arising in autonomous vehicles and decentralized control of unmanned aerial vehicles, we consider multi-agent filtering which multiple agents generate state estimates based on information the objective is to minimize a coupled mean-squared error call team mean-squar...

This paper is concerned with the prediction of the conditional mean which involves the fixed and random effects based on the natural exponential family with a quadratic variance function. The best predictor is interpreted as the Bayes estimator in the Bayesian context, and the empirical Bayes estimator (EB) is useful for small area estimation in the sense of increasing precision of prediction f...

A b s t r a c t. Several results are obtained concerning the function ∆ k (x), which represents the error term in the general Dirichlet divisor problem. These include the estimates for the integral of this function, as well as for the corresponding mean square integral. The mean square integral of ∆ 2 (x) is investigated in detail.