27 research outputs found

    Using Local Correlation to Explain Success in Baseball

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    Statisticians have long employed linear regression models in a variety of circumstances, including the analysis of sports data, because of their flexibility, ease of interpretation, and computational tractability. However, advances in computing technology have made it possible to develop and employ more complicated, nonlinear, and nonparametric procedures. We propose a fully nonparametric nonlinear regression model that is associated to a local correlation function instead of the usual Pearson correlation coefficient. The proposed nonlinear regression model serves the same role as a traditional linear model, but generates deeper and more detailed information about the relationships between the variables being analyzed. We show how nonlinear regression and the local correlation function can be used to analyze sports data by presenting three examples from the game of baseball. In the first and second examples, we demonstrate use of nonlinear regression and the local correlation function as descriptive and inferential tools, respectively. In the third example, we show that nonlinear regression modeling can reveal that traditional linear models are, in fact, quite adequate. Finally, we provide a guide to software for implementing nonlinear regression. The purpose of this paper is to make nonlinear regression and local correlation analysis available as investigative tools for sports data enthusiasts

    The Connection Between Race and Called Strikes and Balls

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    We investigate potential racial bias by Major League Baseball umpires. We do so in the context of the subjective decision as to whether a pitch is called a strike or a ball, using data from the 1989-2010 seasons. We find limited, and sometimes contradictory, evidence that umpires unduly favor or unjustly discriminate against players based on their race. Potential mitigating variables such as attendance, terminal pitch, the absolute score differential, and the presence of monitoring systems do not consistently interact with umpire/pitcher and umpire/hitter racial combinations. Most evidence that would first appear to support racially connected behaviors by umpires appears to vanish in three-way interaction models. Overall, our findings fall well short of convincing evidence for racial bias

    Maximum penalized quasi-likelihood estimation of the diffusion function

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    We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function, we study the asymptotic properties of our estimator by way of simulation. Under the assumption that overnight London Interbank Offered Rates (LIBOR); the USD/EUR, USD/GBP, JPY/USD, and EUR/USD nominal exchange rates; and 1-month, 3-month, and 30-year Treasury bond yields are generated by diffusion processes, we use our numerical scheme to estimate the diffusion function.Comment: 17 pages, 4 figures, revised versio

    Testing Diffusion Processes for Non-Stationarity

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    Financial data are often assumed to be generated by diffusions. Using recent results of Fan et al. (J Am Stat Assoc, 102:618–631, 2007; J Financ Econometer, 5:321–357, 2007) and a multiple comparisons procedure created by Benjamini and Hochberg (J R Stat Soc Ser B, 59:289–300, 1995), we develop a test for non-stationarity of a one-dimensional diffusion based on the time inhomogeneity of the diffusion function. The procedure uses a single sample path of the diffusion and involves two estimators, one temporal and one spatial. We first apply the test to simulated data generated from a variety of one-dimensional diffusions. We then apply our test to interest rate data and real exchange rate data. The application to real exchange rate data is of particular interest, since a consequence of the law of one price (or the theory of purchasing power parity) is that real exchange rates should be stationary. With the exception of the GBP/USD real exchange rate, we find evidence that interest rates and real exchange rates are generally non-stationary. The software used to implement the estimation and testing procedure is available on demand and we describe its use in the paper

    Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry Analysis of Lower Pecos Rock Paints and Possible Pigment Sources

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    Chemical analyses of prehistoric rock paints from the Lower Pecos Region of southwestern Texas were undertaken using laser ablation-inductively coupled plasma-mass spectrometry. This technique allowed us to measure the chemical composition of the paint pigments with minimal interference from a natural rock coating that completely covers the ancient paints. We also analyzed samples representing potential sources of paint pigments, including iron-rich sandstones and quartzite from the study area and ten ochre samples from Arizona. Cluster analysis, principle component analysis and bivariate plots were used to compare the chemical compositions of the paint and pigment sources. The results indicate that limonite extracted from the sandstone was the most likely source for some of the pigments, while ochre was probably used as well

    MATH 111-01, Elementary Probability and Statistics, Fall 2009

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    This syllabus was submitted to the Office of Academic Affairs by the course instructor. Uploaded by Archives RSA Josephine Hill.The seeds of statistics|which is often considered a mathematical science quite distinct from mathematics itself|were sown in the 17th century, with the development of probability theory by Blaise Pascal and Pierre de Fermat. Probability theory itself arose due to interest in games of chance. In contrast to probability theorists (who propose probability models and then study those models with little regard for the random realizations generated by those models), statisticians are interested in the random realizations themselves (called data), and what those random realizations suggest about the parameters that govern the (perhaps unknown) underlying probability models. A critical development in the history of statistics was the method of least squares, which was probably ÂŻrst described by Carl Friedrich Gauss in 1794. Early applications of statistical thinking revolved around the needs of states to base public policy on demographic, economic, and pub- lic health data. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in gov- ernment, business, and the natural and social sciences, and computers are transforming the ÂŻeld at a breathtaking pace. Statistics is widely considered an exciting, dynamic, and intrinsically interdisciplinary science. The work of statisticians powers search engines like Google, has proven critical to the exploration of the human genome, and is used by hedge fund managers to detect arbitrage opportunities (risk-free trading strategies that yield proÂŻt with positive probability) that are successful on average (called statistical arbitrage). The New York Times recently declared that statisticians will enjoy one of the highest-paying, highly-coveted careers over the next decade. I hope you'll enjoy learning a little bit about statistics this semester with me

    MATH 131-01, Mathematics Through Advanced Software, Fall 2010

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    This syllabus was submitted to the Office of Academic Affairs by the course instructor. Uploaded by Archives RSA Josephine Hill.A computer algebra system is a software program that facilitates symbolic mathematics. Though the main purpose of a computer algebra system is manipulation of mathematical expressions in symbolic form, over the past few decades computer algebra systems have evolved to include formidable numerical and data analysis capabilities. By “symbolic manipulation,” I mean simplification of certain expressions to some standard form (with user-designated constraints often being possible). Computer algebra systems permit the user to substitute symbols or numerical values in place of certain expressions, as well as to make changes in the form of those expressions (partial and full factorization, representation as partial fractions, rewriting trigonometric functions in terms of exponential functions, etc.). Many standard tasks of calculus are well-handled by computer algebra systems: the symbolic computation of limits, derivatives, integrals, and infinite sums; symbolic constrained and unconstrained local and global optimization; and the calculation of Taylor expansions of analytic functions. Increasingly, computer algebra systems are being used to power automated theorem-proving and theorem verification, two tasks that are central components of the growing field of experimental mathematics. Mathematica is just one example of a computer algebra system, but there are many others, including Maple, Derive, Reduce, MuPAD, Magma, Axiom, and Maxima. Though proprietary (and, arguably, expensive), Mathematica is the computer algebra system most frequently used at Rhodes College (and, in fact, at many colleges, universities, corporations, and research laboratories). It was originally conceived by Stephen Wolfram, a MacArthur fellow, physicist, and author of A New Kind of Science, as a computer program called SMP (symbolic manipulation program). Mathematica 1.0, the successor to SMP, was released in 1988 and has improved incrementally with new major releases in 1991, 1996, 1999, and 2003. With the release of Mathematica 6.0 in 2007, Mathematica experienced enormous improvements in system stability, software documentation, dynamic interactivity, and data computability. In 2009, Rhodes College upgraded its ten-year-old Mathematica 4.0 license to a new Mathematica 7.0 license. Today at Rhodes College, Mathematica is used for undergraduate and faculty research, projects in upper-level courses in mathematics and the natural sciences, and instruction in Math 115 (applied calculus)

    MATH 111-01/02, Introduction to Statistics, Spring 2010

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    This syllabus was submitted to the Office of Academic Affairs by the course instructor. Uploaded by Archives RSA Josephine Hill.The seeds of statistics—which is often considered a mathematical science quite distinct from mathematics itself—were sown in the 17th century, with the development of probability theory by Blaise Pascal and Pierre de Fermat. Probability theory itself arose due to interest in games of chance. In contrast to probability theorists (who propose probability models and then study those models with somewhat less regard for the random realizations generated by those models), statisticians are interested in the random realizations themselves (called data), and what those random realizations suggest about the parameters that govern the (perhaps unknown) underlying probability models. A critical development in the history of statistics was the method of least squares, which was probably first described by Carl Friedrich Gauss in 1794. Early applications of statistical thinking revolved around the needs of states to base public policy on demographic, economic, and public health data. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and the natural and social sciences. Computers are transforming the field at a breathtaking pace. Statistics is widely considered an exciting, dynamic, and intrinsically interdisciplinary science. The work of statisticians powers search engines like Google, has proven critical to the exploration of the human genome, and is used by hedge fund managers to detect arbitrage opportunities (risk-free trading strategies that yield profit with positive probability) that are profitable only on average (called statistical arbitrage). The New York Times recently declared that statisticians will enjoy one of the highest-paying, highly-coveted careers over the next decade. I hope you’ll enjoy learning a little bit about statistics this semester with me

    Exploring measures of association

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    Using Alt-Click, add additional data points to the scatter plot above or drag the existing data points. The least-squares linear fit to the data changes as you add additional data points or drag them. Additionally, three sample measures of dependence between the X and Y coordinates of the data are summarized (viewing the coordinate projections as realizations from a pair of random variables)Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
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