Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides a complete picture of the relationship between the response variable and covariates by estimating a family of conditional quantile functions. Also, it offers a natural solution to challenges such as; homoscedasticity and sometimes unrealistic normality assumption in the usual conditional mean regression. Most of the results for quantile regression are based on simple random sampling (SRS). In this thesis, we study the quantile regression with rank-based sampling methods. Rank-based sampling methods have a wide range of applications in medical, ecological and environmental research, and have been shown to perform better than SRS in estimating several population parameters. We propose a new objective function which takes into account the ranking information to estimate the unknown model parameters based on the maxima or minima nomination sampling designs. We compare the mean squared error of the proposed quantile regression estimates using maxima (or minima) nomination sampling design and observe that it provides higher relative e ciency when compared with its counterparts under SRS design for analyzing the upper (or lower) tails of the distribution of the response variable. We also evaluate the performance of our proposed methods when ranking is done with error. / February 2017

Each year, admissions officers throughout the United States commit many intense months to reviewing applications to their college/university. According to the College Board, there are established key elements considered in admissions decisions, including grades in college prep courses, standardized test scores, overall academic performance, and class rank. Approximately half of high schools in the U.S. provide class rank, yet it has maintained importance as the number four factor for over a decade, trumping other factors such as extracurricular accomplishments, teacher recommendations, and interviews. A student’s rank-in-class can be used to determine their relative achievement within his or her school, to compare them to the entire applicant pool at a college or university, and to rate students for scholarship selection, along with selections for countless other accolades and financial awards. Rank is calculated across a wide span of methods using grade point averages (GPAs) that sometimes account for course rigor, and sometimes do not. So that colleges/universities might evaluate rigor and competitiveness of each applicant based on the school’s institutional priorities, I contend that colleges/universities should recalculate GPAs as provided from the high school, giving weight to what they value as an institution. Over the past year, I have dramatically shifted my belief in the way rank ought to be used. Earlier in my admissions career, I believed rank was accurate and useful. Now that I have taken significant time to consider the role of rank from the perspective of a school counselor, I realize that it is not the beacon of precision. It has become increasingly clear to me that it is the job of colleges/universities to rank high school students; it is not the job of high schools. During months spent speaking with current and former school counselors, and my own motivation to become a school counselor, I realized that it does not ultimately benefit high schools to provide colleges with rank and it does not benefit colleges to use a precise rank that is born out of one specific context.

In this thesis, we perform analysis and prediction for community structures in graphs using unsupervised learning. The methods we use require the data matrices to be of low rank, and such matrices appear quite often in real world problems across a broad range of domains. Such a modelling assumption is widely considered by classical algorithms such as principal component analysis (PCA), and the same assumption is often used to achieve dimensionality reduction. Dimension reduction, which is a classic method in unsupervised learning, can be leveraged in a wide array of problems, including prediction of strength of connection between communities from unlabeled or partially labeled data. Accordingly, a low rank assumption addresses many real world problems, and a low rank assumption has been used in this thesis to predict the strength of connection between communities in Amazon product data. In particular, we have analyzed real world data across retail and cyber domains, with the focus being on the retail domain. Herein, our focus is on analyzing the strength of connection between the communities in Amazon product data, where each community represents a group of products, and we are given the strength of connection between the individual products but not between the product communities. We call the strength of connection between individual products first order data and the strength of connection between communities second order data. This usage is inspired by [1] where first order time series are used to compute second order covariance matrices where such covariance matrices encode the strength of connection between the time series. In order to find the strength of connection between the communities, we define various metrics to measure this strength, and one of the goals of this thesis is to choose a good metric, which supports effective predictions. However, the main objective is to predict the strength of connection between most of the communities, given measurements of the strength of connection between only a few communities. To address this challenge, we use modern extensions of PCA such as eRPCA that can provide better predictions and can be computationally efficient for large problems. However, the current theory of eRPCA algorithms is not designed to treat problems where the initial data (such as the second order matrix of communities strength) is both low rank and sparse. Therefore, we analyze the performance of eRPCA algorithm on such data and modify our approaches for the particular structure of Amazon product communities to perform the necessary predictions.

This study investigated the acquisition of food by hand-reared coyotes, Canis latrans, of different social rank in a familiar area with and without novel objects (safe and potentially unsafe conditions). The first objective was to test the hypothesis that dominant animals are more hesitant than subordinates in approaching food in the presence of a novel stimulus. The results were that dominant pups usually were the first to feed in the absence of novel stimulus, and subordinate pups were the first to feed when novel objects were present.

Attenuating random and coherent noise is an important part of seismic data processing. Successful removal results in an enhanced image of the subsurface geology, which facilitate economical decisions in hydrocarbon exploration. This motivates the search for new and more efficient techniques for noise removal. The main goal of this thesis is to present an overview of the Singular Spectrum Analysis (SSA) technique, studying its potential application to seismic data processing. An overview of the application of SSA for time series analysis is presented. Subsequently, its applications for random and coherent noise attenuation, expansion to multiple dimensions, and for the recovery of unrecorded seismograms are described. To improve the performance of SSA, a faster implementation via a randomized singular value decomposition is proposed. Results obtained in this work show that SSA is a versatile method for both random and coherent noise attenuation, as well as for the recovery of missing traces. / Geophysics

Theoretical positions (Sloman & Gilbert, 2000), current research (Robbins & Tanck, 1997) and clinical observations (APA, 1994) have generally concluded that depressed populations tend to demonstrate an elevated level of hostility. Based on the premises of the Social Rank Theory (SRT; Sloman & Gilbert, 2000), the current study explores the purported etiological underpinnings of the co-occurrence between depression and hostility. The SRT regards depression as a state of inferiority resulting from a drop in social rank and hostility as stemming from a sense of injustice over this inferiority. To test this idea, measures of perceived social rank, depression, trait anger, anger expression and perceived injustice were administered to 97 university students at two time points, one month apart. Long-term rank change was measured retrospectively at Time 1 and short-term rank change was measured prospectively by sampling at Time 1 and Time 2. Three hypotheses were advanced: 1) social rank would be negatively associated with depression; 2) unfavourable rank change would predict greater levels of depression; and 3) unfavourable rank change from an initially superior rank would predict greater levels of anger and perceived injustice. Results were partially supportive of the hypotheses. As expected, social rank was negatively associated with depression. As well, a long-term change in social rank predicted greater levels of anger suppression. Results were discussed with respect to their consistency with the SRT. Potential weaknesses of the methodology and future directions of this line of inquiry were also presented.

Theoretical positions (Sloman & Gilbert, 2000), current research (Robbins & Tanck, 1997) and clinical observations (APA, 1994) have generally concluded that depressed populations tend to demonstrate an elevated level of hostility. Based on the premises of the Social Rank Theory (SRT; Sloman & Gilbert, 2000), the current study explores the purported etiological underpinnings of the co-occurrence between depression and hostility. The SRT regards depression as a state of inferiority resulting from a drop in social rank and hostility as stemming from a sense of injustice over this inferiority. To test this idea, measures of perceived social rank, depression, trait anger, anger expression and perceived injustice were administered to 97 university students at two time points, one month apart. Long-term rank change was measured retrospectively at Time 1 and short-term rank change was measured prospectively by sampling at Time 1 and Time 2. Three hypotheses were advanced: 1) social rank would be negatively associated with depression; 2) unfavourable rank change would predict greater levels of depression; and 3) unfavourable rank change from an initially superior rank would predict greater levels of anger and perceived injustice. Results were partially supportive of the hypotheses. As expected, social rank was negatively associated with depression. As well, a long-term change in social rank predicted greater levels of anger suppression. Results were discussed with respect to their consistency with the SRT. Potential weaknesses of the methodology and future directions of this line of inquiry were also presented.

Investment of mutual fund has always been popular to the common investor. No matter investing at Systematic Investment Plan or One-time Investment, choosing a ¡§good¡¨ mutual fund is expected for every investor. However, how to find a good one among a large number of funds? In the past reports or theses, there are many reasons of influencing mutual fund performance, which include fund¡¦s size among others. The common sense said that ¡§if you want to invest in mutual fund, you should choose the larger size ¡¨ Is that true? Through the past reports we can find out different opinions. This study mainly research into the relationship between performance and size of domestic open-ended mutual funds. Expect to give a simpler data for reference and lower the risk before general investors put money into funds. The logic of Spearman's Rank Correlation coefficient would be applied as the statistical inference in this study, and the domestic open-ended equity fund, balanced fund, and quasi-money market fund will be used as the observed samples. Monthly performance and size is the observed unit of time in this research period from March 2001 to February 2010. Thus via this mode will know whether the correlation between fund¡¦s performance and size is positive, negative or there is no correlation. The conclusions of this study are presented as follows: 1. There is a low positive correlation between performance and size for equity fund and quasi-money market fund. But the balanced fund does not show any correlation for these two variables. 2. Moreover, the study shows there is better performance for investing in over 4 billion NT asset of equity fund in a short term period. But the result of balanced fund and quasi-money market fund can¡¦t highlight the optimal size in a short term period. 3. From the long term point of view, the optimal interval of size for equity and balanced fund is between 1 billion and 2 billion. And the optimal size to quasi-money market fund is over 40 billion.

The purpose of this study was to analyze the interactions of visitors and Formosan macaques (Macaca cyclopis) at the Mt. Longevity. Data on the attitudes of visitors were collected by using questionnaires covering topics such as purpose, frequency and opinions of visitors. Scan samplings, agonistic behavior samplings and focal samplings were used as observational methods to record the agonistic behaviors of monkeys. The study also analyzed patterns of human-monkey interactions that recorded through ad libitum samplings, including visitor participation that influenced agonistic behaviors among the monkeys. Statistical analyses were used to analyze various factors that influenced agonistic frequency and patterns. The agonistic behaviors in dyads during food provision tests were used to establish their rank relationships and dominance styles. Mt Longevity is a major recreational site in Kaohsiung city; the human pressure on Mt. Longevity was high and the tourist numbers were estimated as 6175 individuals ( ¡Ó 119, n = 10) in holidays and 3490 individuals ( ¡Ó 68, n = 10) in weekdays (between 08:00 to 18:00 hrs). The vegetation cover was apparently reduced above 60% in 16 recreational sites surveyed. The tourist numbers appeared to exceeding the carrying capacity of Mt. Longevity. The frequencies of human-monkey interaction were influenced by the number of monkeys and concentrated during the afternoons; the average frequency was 9.3 times / hr in holiday and 3.3 times / hr in weekday. The average frequency of tourists provisioned for monkeys was 0.59 times / hr ( ¡Ó 17.2, n = 131). An overall ratio of 17.5 : 1 between human-initiated and monkey-initiated interaction behaviors was found. Pass and eye contact accounted for over 67% of these interactions, and adult monkeys participated in human-monkey interaction more than the rest of the age / sex classes. During the conflict between human and macaques, most visitors used sticks or hands / legs to drive adult males away (63.5%). The average daily activities of Formosan macaques were: 37.7% inactive, 24.6% moving, 24.5% affiliation, eating / foraging 9.5% and agonistic behavior 2.6%. Frequencies of monkey aggressive behaviors increased along with increasing individuals of monkeys, and frequencies of their body aggressions and aggressions were higher during provision than without human disturbance. Open mouth threat was the most frequent aggressive behavior expressed by the monkeys (60.0%), while fleeing (37.0%) and squealing (36.0%) were the most common submissive behaviors. Agonistic initiators were mostly adult females (41.9%) and males (40.4%) and agonistic reactors were mostly juveniles (44.6%) and adult females (32.6%). Monkey contest was only 2.8% - 3.9% of total aggressive behaviors and the study revealed that the dominance style of Formosan macaques was despotic social system. The frequency of aggressive behavior of adult males (1.3 ¡Ó 2.1 times / 20min, n = 14) was 2.6 times in average to that of adult females (0.5 ¡Ó 0.9 times / 20min, n = 17). It varied significantly among different adult males and it was higher in mating seasons than the non-mating seasons (p<0.05). However, the frequencies of aggressive behavior of adult females were similar between seasons and among ranks (low, middle and high) but the frequency of submissive behaviors was higher in low rank adult females than that of high rank ones (p<0.05). Adult male and female Formosan macaques had a similar dominance style (aggression, avoidance, ignoring, undecided, AAD pattern and NNI pattern) in food tests; adult males showed more frequent aggression toward adult males than to adult females and juveniles. The individuals who showed open mouth threat had a success rate of getting food for over 50%.

Comparison of two or more failure time distributions based on interval-censored data is tested by extension of log-rank test proposed by Sun (1996, 2001, 2004). Furthermore, Chang (2004) verified that the proposed test statistics are approximately chi-cquare with degrees of freedom p-1 after constants factor adjustment which can be obtained from simulations. In this paper we approach in a different way to estimate the adjustment factor of a given interval-censored data by applying the bootstrap technique to the test statistics. Simulation results indicate that the bootstrap technique performs well on those test statistics except the one proposed in 1996. By using chi-square goodness of fit test, we found that Sun's test in 1996 is significantly far from any chi-square.