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## Scholarly Works (63 results)

An experimental study was conducted on the noise characteristics of four-bladed general aviation propellers with uneven blade spacing. The subscale propeller designs were inspired by the fourbladed McCauley propellers used on the Beechcraft King Air 350 series aircraft. The 4-inch diameter (1:22.5 scale) propellers were manufactured using high-resolution stereolithography and were powered by a high performance, radio controlled brushless electric motor. Acoustic measurements were taken with a 24-microphone array. The use of uneven blade spacing created additional tones over which the acoustic intensity was distributed. Large amounts of acoustic intensity were shifted into the lowest frequency tone (occuring at half of the blade passage frequency of the propeller with evenly spaced blades), resulting in reductions of A-weighted overall sound pressure levels of up to 5 dB for polar angles near 90. These reduction are partly offset by increases in A-weighted overall sound pressure levels of up to 4 dB at polar angles less than 50. Although the theory used to predict propeller noise does not show good agreement with experiments, it does show this trend of increasing noise at low polar angles. Since noise at low polar angles are weighted less in noise metrics such as flyover noise, the use of uneven blade spacing has potential for providing noise reduction without adding excessive complexity to propeller design.

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point and prove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward a datadependent point turns out to be equivalent to combining two random variables using the James-Stein rule. We propose a general combination scheme which includes random combination (the James-Stein combination) and the usual nonrandom combination as special cases. As an example, we apply our method to combine the Least Absolute Deviations estimator and the Least Squares estimator. Our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are drawn from symmetric distributions. Finally, using stock return data we present some empirical evidence that the combination estimators have the potential to improve out-of-sample prediction in terms of both mean square error and mean absolute error.

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point and prove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward a data-dependent point turns out to be equivalent to combining two random variables using the James-Stein rule. We propose a general combination scheme which includes random combination (the James-Stein combination) and the usual nonrandom combination as special cases. As an example, we apply our method to combine the Least Absolute Deviations estimator and the Least Squares estimator. Our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are drawn from symmetric distributions. Finally, using stock return data we present some empirical evidence that the combination estimators have the potential to improve out-of-sample prediction in terms of both mean square error and mean absolute error.

For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and excess kurtosis. This stylized fact has been supported by a vast collection of empirical studies. Given that the conventional measures of skewness and kurtosis are computed as an average and that averages are not robust, we ask, "How useful are the measures of skewness and kurtosis used in previous empirical studies?" To answer this question we provide a survey of robust measures of skewness and kurtosis from the statistics literature and carry out extensive Monte Carlo simulations that compare the conventional measures with the robust measures of our survey. An application of the robust measures to daily S&P500 index data indicates that the stylized facts might have been accepted too readily. We suggest that looking beyond the standard skewness and kurtosis measures can provide deeper insight into market returns behaviour.

Demand for a small, portable IR spectrometer has been growing steadily for many years. A monochromator is one of the essential parts that comprises any spectroscopy system. A MEMS-based, tunable Fabry-Perot interferometer filter (FPI), that is proposed to be a monochromator with a broadband IR detector array in an improvised explosive device detection system, is designed, simulated, fabricated and characterized in this dissertation. With the operational wavelength range in the long wavelength IR region, from 8 to 11 µm, a distributed Bragg reflector with germanium and zinc sulfide is used to implement the mirror that covers the target spectrum. One of the mirrors is fabricated with four beam springs in an X-shape to tune the passing wavelength of the FPI filter by adjusting the gap distance between two membranes using electrostatic attraction.

Designed device is simulated to confirm it meeting the required device specification. Taking advantage of SOI wafer, the FPI filter is fabricated with simple fabrication process with only four lithography masks, one deposition, and three etch steps. The scaffold structure is fabricated with both surface micromachining and bulk micromachining process. The DBR mirror is deposited using EBPVD on two membranes, and then assembled into the FPI filter. The fabrication process is performed at the Stanford Nanofabrication Facility (SNF). Fabricated device is characterized at the UCSC and the SNF. Completed FPI filter showed the necessary filtering and tuning behavior with 30% transmittance peak and 2 µm FWHM. With expected performance of 100% peak and 0.15 µm FWHM, however, a need for significant performance improvement is observed. The cause of transmission peak degradation is attributed to the loss due to reflection and absorption of Si membrane and of passband broadening to the plate defeats of the DBR. The direction of study for further process improvement is suggested.

We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point and prove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward a data-dependent point turns out to be equivalent to combining two random variables using the James-Stein rule. We propose a general combination scheme which includes random combination (the James-Stein combination) and the usual nonrandom combination as special cases. As an example, we apply our method to combine the Least Absolute Deviations estimator and the Least Squares estimator. Our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are drawn from symmetric distributions. Finally, using stock return data we present some empirical evidence that the combination estimators have the potential to improve out-of-sample prediction in terms of both mean square error and mean absolute error.

To date the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain "pseudo-true" parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.