Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Solar Forcing of Gulf of California Climate During The Past 2000 Yr Suggested by Diatoms and Silicoflagellates

High-resolution records of the past 2000 yr are compared in a north–south transect (28° N to 24° N) of three cores from the eastern slopes of the Guaymas, Carmen, and Pescadero Basins of the Gulf of California (hereafter referred to as the “Gulf”). Evenly-spaced samples from the varved sediments in each core allow sample resolution ranging from ∼ 16 to ∼ 37 yr. Diatoms and silicoflagellates capture the seasonal variation between a late fall to early spring period of high biosiliceous productivity, that is driven by northwest winds, and a summer period of warmer, more stratified waters during which these winds slacken and/or reverse direction (monsoonal flow). As these winds decrease, tropical waters enter the Gulf and spread northward. Individual samples represent a composite of 7 to 23 yr of deposition and are assumed to record the relative dominance of the winter vs. summer floral components. Intervals of enhanced summer incursion of tropical waters, alternating with periods of increased late fall to early spring biosiliceous productivity are recorded in all three cores. Regularly spaced cycles (∼ 100 yr duration) of Octactis pulchra, a silicoflagellate proxy for lower SST and high productivity, and Azpeitia nodulifera, a tropical diatom, occur between ∼ A.D. 400 and ∼ 1700 in the more nearshore Carmen Basin core, NH01-21 (26.3° N), suggesting a possible solar influence on coastal upwelling. Cores BAM80 E-17 (27.9° N) and NH01-26 (24.3° N) contain longer-duration cycles of diatoms and silicoflagellates. The early part of Medieval Climate Anomaly (∼ A.D. 900 to 1200) is characterized by two periods of reduced productivity (warmer SST) with an intervening high productivity (cool) interval centered at ∼ A.D. 1050. Reduced productivity and higher SST also characterize the record of the last ∼ 100 to 200 yr in these cores. Solar variability appears to be driving productivity cycles, as intervals of increased radiocarbon production (sunspot minima) correlate with intervals of enhanced productivity. It is proposed that increased winter cooling of the atmosphere above southwest U.S. during sunspot minima causes intensification of the northwest winds that blow down the Gulf during the late fall to early spring, leading to intensified overturn of surface waters and enhanced productivity. A new silicoflagellate species, Dictyocha franshepardii Bukry, is described and illustrated.

Selection of Switching Sites in All-Optical Nework Topology Design

In this paper, we consider the problem of topology design for optical networks. We investigate the problem of selecting switching sites to minimize total cost of the optical network. The cost of an optical network can be expressed as a sum of three main factors: the site cost, the link cost, and the switch cost. To the best of our knowledge, this problem has not been studied in its general form as investigated in this paper. We present a mixed integer quadratic programming (MIQP) formulation of the problem to find the optimal value of the total network cost. We also present an efficient heuristic to approximate the solution in polynomial time. The experimental results show good performance of the heuristic. The value of the total network cost computed by the heuristic varies within 2% to 21% of its optimal value in the experiments with 10 nodes. The total network cost computed by the heuristic for 51% of the experiments with 10 node network topologies varies within 8% of its optimal value. We also discuss the insight gained from our experiments.