Maximum variance unimodal distributions

A new sufficient condition for the variance of a unimodal distribution in ?a, b? to have the least upper bound $\text{(b ? a)}{}^2\text{12}$ is derived. This condition is more general than the condition found by Jacobson (1969). A new proof that the least upper bound for all unimodal distributions in ?a, b? is $\text{(b ? a)}{}^2\text{9}$ is also given. These results are used to construct a new estimator of the variance of such distributions.     

The L2-optimal cell width for the histogram

We give the value of the cell width which minimizes the integrated mean squared error of the histogram estimate of a multivariate density.     

Limit theorems for the median deviation

Summary In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.     

Variational parameter estimation for a two-dimensional numerical tidal model

It is shown that the parameters in a two-dimensional (depth-averaged) numerical tidal model can be estimated accurately by assimilation of data from tide gauges. The tidal model considered is a semi-linearized one in which kinematical non-linearities are neglected but non-linear bottom friction is included. The parameters to be estimated (bottom friction coefficient and water depth) are assumed to be position-dependent and are approximated by piecewise linear interpolations between certain nodal values. The numerical scheme consists of a two-level leapfrog method. The adjoint scheme is constructed on the assumption that a certain norm of the difference between computed and observed elevations at the tide gauges should be minimized. It is shown that a satisfactory numerical minimization can be completed using either the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm or Nash's truncated Newton algorithm. On the basis of a number of test problems, it is shown that very effective estimation of the nodal values of the parameters can be achieved provided the number of data stations is sufficiently large in relation to the number of nodes.     

Optimizing inputs for diagnosis of diabetes. I. Fitting a minimal model to data

A glucose tolerance test was performed on dogs by injecting glucose intravenously and measuring the plasma glucose and insulin concentrations versus time. Various analytical and computational techniques were utilized to fit the data to a minimal model and to estimate the parameters of the blood glucose regulation process. A relatively good fit was obtained in spite of the rather simple model.Animal experiments were funded by the National Institute of Health Grant No. AM-17236 awarded to Dr. R. N. Bergman at U.S.C.     

Optimal estimation of eddy viscosity for a quasi-three-dimensional numerical tidal and storm surge model

It is shown that the eddy viscosity profile in a quasi-three-dimensional numerical tidal and storm surge model can be estimated by assimilation of velocity data from one or more current meters located on the same vertical line. The computational model used is a simplified version of the so-called vertical/horizontal splitting algorithm proposed by Lardner and Cekirge. We have estimated eddy viscosity both as a constant and as a variable parameter. The numerical scheme consists of a two-level leapfrog method to solve the depth-averaged equations and a generalized Crank-Nicolson scheme to compute the vertical profile of the velocity field. The cost functional in the adjoint scheme consists of two terms. The first term is a certain norm of the difference between computed and observed velocity data and the second term measures the total variation in the eddy viscosity function. The latter term is not needed when the data are exact for the model but is necessary to smooth out the instabilities associated with ‘noisy’ data. It is shown that a satisfactory minimization can be accomplished using either the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm or Nash's truncated Newton algorithm. Very effective estimation of eddy viscosity profiles is shown to be achieved even when the amount of data is quite small.     

Adaptive bandwidth management in ATM networks

A framework for adaptive bandwidth management in ATM based networks is proposed. It is based on a layered approach which includes bandwidth allocation to virtual networks. The central concept of this approach is adaptive estimation of the effective bandwidth required, by connections carried in the network. To achieve reliable results the estimation process takes into account both the traffic source declarations and the connection superposition process measurements on the network links. This is done in an optimization framework provided by estimation theory. A study, based on a linear two-state Kalman filter, shows that the proposed approach provides good adaptation to undeclared changes in traffic parameters and that the network performance is significantly improved when compared to the effective bandwidth allocation based solely on the source parameters declarations. These features allow more relaxed source parameter declarations and at the same time permit less stringent source policing. Thus the two bottlenecks influencing bandwidth management in ATM networks can be significantly widened.     

Minimum information estimation of allocation models of different sizes

For allocation models consisting of n = 10, 6 and 4 equations, constrained generalized least squares coefficient estimates are compared with those obtained from the minimum information (MI) criterion in the sense of statistical information theory. The MI estimates are more efficient for n = 10. The bootstrap procedure is illustrated for the assessment of the variability of these estimates.     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.     

Curve fitting and identification of physical spectra

A modification of the trust-region Gauss-Newton method for the identification of physical spectra is described and analysed. Local convergence results are presented.