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## The Spectral Analysis of Stationary Interval Functions

### Selected Works of David Brillinger (2012-01-01): 25-55 , January 01, 2012

We consider stationary. additive. interval functions X(Δ). These are vector valued stochastic processes having real intervals Δ = (α, β] as domain, having finite dimensional distributions invariant under time translation and satisfying

## The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting

### TEST (2015-06-01) 24: 386-416 , June 01, 2015

In this paper the authors show how it is possible to establish a common structure for the exact distribution of the main likelihood ratio test (LRT) statistics used in the complex multivariate normal setting. In contrast to what happens when dealing with real random variables, for complex random variables it is shown that it is possible to obtain closed-form expressions for the exact distributions of the LRT statistics to test independence, equality of mean vectors and the equality of an expected value matrix to a given matrix. For the LRT statistics to test sphericity and the equality of covariance matrices, cases where the exact distribution has a non-manageable expression, easy to implement and very accurate near-exact distributions are developed. Numerical studies show how these near-exact distributions outperform by far any other available approximations. As an example of application of the results obtained, the authors develop a near-exact approximation for the distribution of the LRT statistic to test the equality of several complex normal distributions.

## Gravitational Antenna Bandwidths and Cross Sections

### Gravitational Wave Data Analysis (1989-01-01) 253: 195-199 , January 01, 1989

Elastic solid antennas are considered. It is shown that many body coherence effects lead to cross sections for pulses, much larger than earlier estimates. For monochromatic continuous signals, the new approach gives the same cross sections as derived in 1960.

A new method for data recording and analysis is proposed. This gives bandwidths several orders larger than are available by recording the output of an optimal filter.

Means are suggested for cascading half acoustic wavelength antennas to give increased cross sections.

Very low temperatures offer methods for selection of antenna quantum states, which imply that the signal to noise ratio can be increased beyond any presently conceived limit.

## Remarks on the Burgers Equation

### Selected Works of Murray Rosenblatt (2011-01-01): 231-238 , January 01, 2011

Periodic and aperiodic solutions of the Burgers equation
$$u_t + uu_x=\mu u_{xx}, \ \mu > 0,$$
are studied in this paper. A harmonic analysis of the solutions is carried out and the form of the spectrum is estimated for large time. Corresponding estimates of energy decay are also made, In Burgers’ work on this equation. the case in which
$$\mu \downarrow 0$$
with *t* fixed, and one then lets *t*→∞, is studied. In our investigation, a fixed value of *μ* > 0 is taken and then one lets *t*→∞. A similar analysts is also carried out for an irrotaticnal solulion of a similar 3-dimensionat system of equations. For large time and moderate wavenumbers there is. to the first order. a drift of spectral mass from low wavenumbers to higher wavenumbers. Comments are also made on the asymptotic distribution of a class of random solutions.

## Statistical properties of large published classifications

### Journal of Classification (1992-12-01) 9: 187-210 , December 01, 1992

Large published classifications typically consist of sets (called taxa) hierarchically arranged according to taxonomic rank. A statistical survey of 23 such classification reveals the following distinctive properties. The pattern of mandatory and optional taxonomic ranks is similar to a Guttman scale. Mean taxon size (defined as the number of next-lower-rank taxa per higher-rank taxon) is a U-shaped function of mandatory rank, and averages about seven across ranks with no significant differences between classifications. The variability of taxon size is a decreasing function of mandatory rank. The generality of these properties across classifications suggests that they are determined by the psychology of the classification process. In contrast, there are significant differences between classifications in the variability of taxon size and in the prevalence of optional ranks, both of which are greater in biological than in nonbiological classifications. These differences may reflect the nature of the materials classified.

## Asymptotic Expansions for the Power of Distributionfree Tests in the Two-Sample Problem

### Selected Works of Willem van Zwet (2012-01-01): 117-184 , January 01, 2012

Asymptotic expansions are established for the power of distributionfree tests in the two-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann for distributionfree tests with respect to their parametric competitors and for the estimators of shift associated with these tests.

## Subsampling Stock Returns

### Subsampling (1999-01-01): 291-314 , January 01, 1999

There has been considerable debate in the recent finance literature over whether stock returns are predictable. A number of studies appear to provide empirical support for the use of the current dividend-price ratio, or dividend yield, as a measure of expected stock returns (see, for example, Rozeff, 1984; Campbell and Shiller, 1988b; Fama and French, 1988; Hodrick, 1992; and Nelson and Kim, 1993). The problem with such studies is that stock return regressions face several kinds of statistical problems, among them strong dependency structures and biases in the estimation of regression coefficients. These problems tend to make findings against the no predictability hypothesis appear more significant than they really are. Having recognized this, Goetzmann and Jorion (1993) argue that previous findings might be spurious and are largely due to the poor small sample performance of commonly used inference methods. They employ a bootstrap approach and conclude that there is no strong evidence indicating that dividend yields can be used to forecast stock returns. One should note, however, that their special approach is not shown to be backed up by theoretical properties. Also, it requires a lot of custom-tailoring to the specific situation at hand. For other scenarios, a different tailoring would be needed.

## The role of Ugandan District Hospital orthopedic units in the care of vulnerable road users: a cross-sectional study

### Injury Epidemiology (2016-12-05) 3: 1-8 , December 05, 2016

### Background

Musculoskeletal injuries are a common cause of morbidity after road traffic injury (RTI) in motorizing countries. District hospitals provide front-line orthopedic care in Uganda and other sub-Saharan African nations. Improving care at the district hospital level is an important component of the World Health Organization’s strategy for surgical and trauma systems strengthening, but the data necessary to inform RTI safety and care initiatives has previously been insufficient at the district hospital level. The objective of this study was to provide data on the patient population and patterns of musculoskeletal injury caused by RTI at Ugandan district hospitals.

### Methods

In this cross-sectional study, all patients with musculoskeletal injuries identified on x-ray presenting to three Ugandan district hospitals from October 2013 to January 2014 were interviewed and examined to obtain data on patient demographics and injury context by road user category. This manuscript is a sub-group analysis of RTI victims from a broader dataset of all musculoskeletal injuries.

### Results

Vulnerable road users comprised 92 % of musculoskeletal RTI patients, with 49 % (95 % CI 41–57 %) pedestrians, 41 % (95 % CI 33–49 %) motorcyclists, and 2 % (95 % CI 0–4 %) cyclists. Commonly injured subgroups included student pedestrians (33 % (95 % CI 22–44 %) of pedestrians) and motorcyclists with less than a post-secondary education (74 % (95 % CI 63–85 %) of motorcyclists). The morning hours were the most common time of injury for all RTI patients (37 %%; 95 % CI 30–44 %) and motorcyclists (46 %; 95 % CI 34–58 %), while pedestrians were most commonly injured in the evening (32 %; 95 % CI 21–43 %).

### Conclusions

By demonstrating commonly injured demographic groups and high frequency times of day for injury, this surveillance study of musculoskeletal RTI suggests targeted avenues for future road safety research in the districts of Uganda. Compared with previous studies from the capital of Uganda, these results suggest that Ugandan district hospitals care for a disproportionate share of vulnerable road users, a discrepancy which may pertain to other sub-Saharan African nations, as well. Strengthening district hospital orthopedic care should be considered a priority of strategies aimed at improving outcomes for these vulnerable groups.

## Bayesian inferences for receiver operating characteristic curves in the absence of a gold standard

### Journal of Agricultural, Biological, and Environmental Statistics (2006-06-01) 11: 210-229 , June 01, 2006

Sensitivity and specificity are used to characterize the accuracy of a diagnostic test. Receiver operating characteristic (ROC) analysis can be used more generally to plot the sensitivity versus (1-specificity) over all possible cutoff points. We develop an ROC analysis that can be applied to diagnostic tests with and without a gold standard. Moreover, the method can be applied to multiple correlated diagnostic tests that are used on the same individual. Simulation studies were performed to assess the discrimination ability of the no-gold-standard method compared with the situation where a gold standard exists. We used the area under the ROC curve (AUC) to quantify the diagnostic accuracy of tests and the difference between AUCs to compare their accuracies. In particular, we can estimate the prevalence of disease/infection under the no-gold-standard method. The method we proposed works well in the absence of a gold standard for correlated test data. Correlation affected the width of posterior probability intervals for these differences. The proposed method was used to analyze ELISA test scores for Johne’s disease in dairy cattle.