An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the...

Using the <italic>DD</italic>-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it <italic>DD</italic>-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be...

Assuming that X1, ..., Xn is a random sample of lifetimes from a distribution with density [latin small letter f with hook] subject to random right-censoring, an estimator of the score function. [latin small letter f with hook]'(x)/[latin small letter f with hook](x), is then proposed and proved...

The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of Asset Pricing -Discrete Time Approach- is to provide a...

Let {Xn} be a strictly stationary [phi]-mixing process with [Sigma]j=1[infinity] [phi]1/2(j) [infinity]. It is shown in the paper that if X1 is uniformly distributed on the unit interval, then, for any t [set membership, variant] [0, 1], Fn-1(t) - t + Fn(t) - t = O(n-3/4(log log n)3/4) a.s. and...

While local governments are increasingly being vested with control over funds for public goods, concern over the capture of decentralized funds by local elites has led decentralization to be combined with central mandates which require a certain proportion of funds to directly benefit the poor....

Certain results on large deviation probabilities for linear and m-dependent processes are considered here.

It is shown in this note that the one-term Edgeworth expansion for the standardized sample mean of n independent lattice random vectors when perturbed by a random variable (1/[radical sign]n) U is the same as in the strongly non-lattice case, where U is a bounded random variable depending only...

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results...