Wantagh Union Free School District and Wantagh Registered Professional Nurses Association

WANTAGH UNION FREE SCHOOL DISTRICT, Employer, and WANTAGH REGISTERED PROFESSIONAL NURSES ASSOCIATION, Union. Case No. M2008-191.m2008_191.pdf: 333 downloads, before Oct. 1, 2020

The sign of the logistic regression coefficient

Let Y be a binary random variable and X a scalar. Let $\hat\beta$ be the maximum likelihood estimate of the slope in a logistic regression of Y on X with intercept. Further let $\bar x_0$ and $\bar x_1$ be the average of sample x values for cases with y=0 and y=1, respectively. Then under a condition that rules out separable predictors, we show that sign($\hat\beta$) = sign($\bar x_1-\bar x_0$). More generally, if $x_i$ are vector valued then we show that $\hat\beta=0$ if and only if $\bar x_1=\bar x_0$. This holds for logistic regression and also for more general binary regressions with inverse link functions satisfying a log-concavity condition. Finally, when $\bar x_1\ne \bar x_0$ then the angle between $\hat\beta$ and $\bar x_1-\bar x_0$ is less than ninety degrees in binary regressions satisfying the log-concavity condition and the separation condition, when the design matrix has full rank.Comment: 9 pages, 0 figure

Impulse TDR and its application to measurement of antennas

The traditional stimulus signal used in a time-domain reflectometer (TDR) is a voltage step. We propose an alternative technique, whereby an impulse generator is employed in place of the step generator in a TDR. The advantage conferred by “impulse TDR” is that more energy is available at higher frequencies than with conventional step TDR, and so a higher bandwidth and signal-to-noise ratio (SNR) is achieved. The theoretical result is compared with measurement

Construction of weakly CUD sequences for MCMC sampling

In Markov chain Monte Carlo (MCMC) sampling considerable thought goes into constructing random transitions. But those transitions are almost always driven by a simulated IID sequence. Recently it has been shown that replacing an IID sequence by a weakly completely uniformly distributed (WCUD) sequence leads to consistent estimation in finite state spaces. Unfortunately, few WCUD sequences are known. This paper gives general methods for proving that a sequence is WCUD, shows that some specific sequences are WCUD, and shows that certain operations on WCUD sequences yield new WCUD sequences. A numerical example on a 42 dimensional continuous Gibbs sampler found that some WCUD inputs sequences produced variance reductions ranging from tens to hundreds for posterior means of the parameters, compared to IID inputs.Comment: Published in at http://dx.doi.org/10.1214/07-EJS162 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org