An Improved Approximation to the Distributions in GMM Estimation

The empirical saddlepoint distribution provides an approximation to the sampling distributions for the GMM parameter estimates and the statistics that test the overidentifying restrictions. The empirical saddlepoint distribution permits asymmetry, non-normal tails, and multiple modes. If identification assumptions are satisfied as the sample size grows the empirical saddlepoint distributions converges to the familiar asymptotic normal distributions. Formulas are given to transform from the moment conditions used in GMM estimation to the estimation equations needed for the saddlepoint approximation. Unlike the absolute errors associated with the asymptotic normal distributions and the bootstrap, the empirical saddlepoint has a relative error. This provides a more accurate approximation to the sampling distribution, particularly in the tails. The calculation of the empirical saddlepoint approximation is computer intensive. The calculations are comparable to the bootstrap and requires repeatedly solving nonlinear equations. The structure of the saddlepoint equation permit analytically first and second derivatives.

The Empirical Saddlepoint Estimator

We define a moment-based estimator that maximizes the empirical saddlepoint (ESP) approximation of the distribution of solutions to empirical moment conditions. We call it the ESP estimator. We prove its existence, consistency and asymptotic normality, and we propose novel test statistics. We also show that the ESP estimator corresponds to the MM (method of moments) estimator shrunk toward parameter values with lower estimated variance, so it reduces the documented instability of existing moment-based estimators. In the case of just-identified moment conditions, which is the case we focus on, the ESP estimator is different from the MM estimator, unlike the recently proposed alternatives, such as the empirical-likelihood-type estimators

Anolis bahorucoensis

Number of Pages: 3Integrative BiologyGeological Science

Not a Victim: Challenges of Providing Services to Sexually Exploited Youth

The number of youth that have been sexually exploited continues to rise. In order to better understand the barriers sexually exploited youth may encounter when trying to seek services, this study explores social workers\u27 perspectives on why these barriers exist. Qualitative interviews were used to gather the experience of social workers who have worked with sexually exploited youth. Six themes consistent with research emerged; these themes are: characteristics of the girls, victim status, lack of awareness, support services, systemic responses and Minnesota responses. These themes show the various reasons youth may not seek services. Implications for clinical practice and future research are discussed

AN ANALYSIS OF BEN MOORE’S COMEDY SONGS USING J. PETER BURKHOLDER’S MUSIC-BORROWING TECHNIQUES

Ben Moore\u27s comedy songs have found favor as the final song on recitals due to their humor. In addition to those themes, the songs have continued a compositional style using music-borrowing techniques. J. Peter Burkholder was the first researcher to codify a set of specific techniques outside the designation of quotation or parody. Using the methodology of Burkholder, Moore\u27s comedy songs and their uses of existing music can be analyzed and situated in the musical borrowing field of study. The techniques found in Moore’s songs include paraphrase, quotation, stylistic allusion, quodlibet, and interjection. Paraphrase is when the borrowed music is altered from the existing music through changes in words, rhythm, or melody. Quotation occurs when a direct extrapolation from the original source is included in the new piece. Stylistic allusion references the music of a particular historical period or composer rather than a specific work. Quodlibet is when several borrowing techniques are used simultaneously or in quick succession. Interjection, a technique I defined, is when borrowed music interrupts the flow of the music and is short in duration. Though Moore\u27s contemporaries also use borrowing techniques, his comedic intent is unique to his songs and sets him apart from other contemporary composers of art songs. Analyzing each comedy song\u27s range, tessitura, and composer\u27s interpretation notes, in addition to defining and outlining the various music-borrowing techniques, demonstrates the differences in these compositions. This document will provide a performer\u27s guide to each piece by showing the intent of each borrowing technique, thus allowing the performer to understand the comedic moments more thoroughly

The Alexander Hamilton and Slavery Debate

Alexander Hamilton, one of the original founding fathers, has been under scrutiny by historians for several years over his belief on the issue of slavery. Hamilton was one of the most influential people in the framing of the Constitution. He wrote many letters back and forth to James Madison while they wrote the Federalist Papers. Hamilton’s opinion on the issue of slavery, unlike Madison’s, is somewhat of a mystery. Some historians argue he was against slavery in principle and the presence of it in the United States, others say he supported slavery in its entirety. Evidences for both sides of the argument are present, but the most recent scholarly arguments, which have come within the last decade, argue that Hamilton personally opposed slavery. However, he chose to follow the law on things such as returning a slave to their owner. When asking a non-historian, “Who was Alexander Hamilton?” Most people are going to say either “The guy on the ten-dollar bill” or “The guy who got shot by the other guy in a duel.” Though he is known for these two things (being on the ten-dollar bill and his death from a duel with Aaron Burr), Alexander Hamilton was much more than these two things. He was a man of many talents. During the American Revolution, he was, through his many political connections in New York, an aide for generals Nathaniel Greene, Henry Knox, and his favorite, General George Washington. Much like Marquis De Lafayette, Hamilton was thought of as a son that George Washington never had

Status Versus Behavior

The central issue regarding the Equal Rights Amendment has been posed as whether men and women should have equal status. A more fundamental question is whether social decisions must be based on status rather than behavior-and must is the proper word when speaking of a constitutional amendment

Not a Victim: Challenges of Providing Services to Sexually Exploited Youth

The number of youth that have been sexually exploited continues to rise. In order to better understand the barriers sexually exploited youth may encounter when trying to seek services, this study explores social workers’ perspectives on why these barriers exist. Qualitative interviews were used to gather the experience of social workers who have worked with sexually exploited youth. Six themes consistent with research emerged; these themes are: characteristics of the girls, victim status, lack of awareness, support services, systemic responses and Minnesota responses. These themes show the various reasons youth may not seek services. Implications for clinical practice and future research are discussed