A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

A common problem in multiple regression analysis is having to engage in a bias variance trade-off in order to maximize the performance of a model. A number of methods have been developed to deal with this problem over the years with a variety of strengths and weaknesses. Of these approaches the ridge estimator is one of the most commonly used. This paper conducts an examination of the properties of the ridge estimator and several alternatives in both deterministic and stochastic environments. We find the ridge to be effective when the sample size is small relative to the number of predictors. However, we also identify a few cases where some of the alternative estimators can outperform the ridge estimator. Additionally, we provide examples of applications where these cases may be relevant.

We have determined the seismic crustal structure of the northern part of the Gorda Ridge using signals generated by explosive charges and recorded on Ocean Bottom Seismometers. The shot pattern forms two parallel lines, one on the east flank and the other along the median valley. Inversion of the travel time data and synthetic modelling of the signals resulted in two compressional velocity structures: the model for the flank indicates a 1.6 km thick upper crust characterized by high velocity gradients and 3.6 km thick lower crust characterized by a low gradient. A sharp mantle transition exists at 5.2 km depth with an upper mantle velocity of 7.6 km/sec. The median valley velocity model has a thicker high gradient upper crust of 3.0 km and a lower crust of at least 3.5 km thickness. No upper mantle velocities were detected beneath the median valley. We have also monitored the seismicity of the ridge during 15 days with two arrays of OBS and detected ~4 events/hour. Epicentral coordinates were determined for 140 earthquakes. Most of them lie within the median valley and show spatial clustering. Intraplate seismicity was also detected in the Gorda Basin with three of the earthquakes big enough to be reported by land stations. They suggest that the Gorda Plate is presently undergoing deformation. Good control over the focal depth was possible for ~80 earthquakes occurring on the ridge, and there the seismic activity appears to be pervasive throughout the upper 20 km suggesting that the the brittle lithosphere is at least this thick. From the earthquake shear-wave data we have obtained a value of 1.73 for the Vp/Vs ratio. Moments of the well constrained events derived from the spectra of the waveforms are of the order 10²⁰ dyne-cm and suggest an average fault width of 300 m. The refraction data is consistent with the earthquake results, and all the evidence suggests that a large magma chamber underlying the axis of spreading does not presently exist at shallow depths. / Graduation date:1985

The seismicity at the northern section of the Gorda Ridge has been studied with Ocean Bottom Seismographs. Nearly one hundred earthquakes were located with RMS travel time residuals less than 0.5 seconds. Most of these events lie within or near the array and they are probably associated with the dynamics of crustal formation which creates the observed bench-like features in the Gorda Ridge. An average of 5 microtremors per hour can be detected in the median valley with a lower activity outside of the ridge. Considerable clustering in time can be seen and it is typical of a main-shock sequence with the largest shock at or very near the beginning followed by a progressive decay in number. Clustering was spatial as well as temporal and the records indicate that they have similar mechanisms. A brittle zone of 18 km thickness at 42°N and 13 km at 42.5°N was found implying any possible magma chamber must be at greater depth. These thicknesses are larger than those observed in the Mid Atlantic ridge and in the East Pacific Rise. They may be explained by the depression of isotherms due to the heat lost by the contact of the ridge with the old and cold plates across the Blanco and the Mendocino Fracture Zones. Comparison of earthquakes locations using only OBS with those obtained from land stations indicate a major P-delay for the Gorda Basin. The seismic activity appears to decrease markedly to the south of 42°N. This drop in activity indicates that the southern part of the ridge is more stable than the northern part. This decrease in activity is not consistent with a southward propagating rift if we accept that higher seismicity levels are expected at the tip of the propagating ridge segments. / Graduation date: 1982

Thesis (M.S.)--University of Hawaii at Manoa, 2006. / Includes bibliographical references (leaves 67-71). / ix, 71 leaves, bound ill., map 29 cm

Würzburg, Univ., Diss., 2009.

The rocks underlying Vulcan Ridge are mainly Proterozoic metasediments of the Lower and Middle Division of the Aldridge formation and Proterozoic (or later) Moyie intrusives. Most of the metasediments are fine-grained quartzites, phyllites, schists and hormfelses composed mainly of quartz, biotite, muscovite and little feldspar. Tourmaline is a minor constituent of most metasediments but in the upper part of the Lower Aldridge it commonly forms up to 30 percent of the rocks. It is believed to have formed metasomatically by solutions derived from the White Creek batholith. A lens-like deposit of breccia-conglomerates makes up the upper most part of the Lower Aldridge. Most of the deposit is composed of unsorted material - angular to subangular fragments of Aldridge type metasediments imbedded in abundant fine-grained matrix of similar composition. This deposit is believed to have formed by subaqueous slides or mudflows. The Moyie intrusives are sill-like bodies of dioritic and gabbroic rocks composed essentially of hornblende, plagioclase and variable amounts of quartz. Most of the variations in texture and composition apparent in some of the intrusives are probably due to alteration but some may also be due to magmatic differentiation and to assimilation of country-rocks. The metasediments in the southern part of the area have been subjected to regional metamorphism and are of low metamorphic grade. In the northern part of the area the rocks have been contact metamorphosed. Within approximately 1½ mile of the White Creek batholith they have been metamorphosed to phyllites, schists and hornfelses which attained or closely approached a medium grade of metamorphism characteristic of the hornblende hornfels facies. Retrogressive metamorphism is extensive in the rocks near the contact of the batholith and is attributed to hydro-thermal solutions derived from that intrusive. Structure of the rocks south of the White Creek batholith is dominated by northeasterly trending folds which have been refolded into a large anticline near the batholith, and by northeasterly striking, steep dipping faults. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Ordinary Least Squares (OLS) models are popular tools among field scientists, because they are easy to understand and use. Although OLS estimators are unbiased, it is often advantageous to introduce some bias in order to lower the overall variance in a model. This study focuses on comparing ridge regression and the LASSO methods which both introduce bias to the regression problem. Both approaches are modeled after the OLS but also implement a tuning parameter. Additionally, this study will compare the use of two different functions in R, one of which will be used for ridge regression and the LASSO while the other will be used strictly for the LASSO. The techniques discussed are applied to a real set of data involving some physiochemical properties of wine and how they affect the overall quality of the wine.