Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Estimation for the general sample selection models

Consider a general regression model with an arbitrary and unknown link function and a stochastic selection variable that determines whether the outcome variable is observable or missing. The paper proposes U-statistics that are based on kernel functions as estimators for the directions of the parameter vectors in the link function and the selection equation, and shows that these estimators are consistent and asymptotically normal.

Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

New Algorithms for M-Estimation of Multivariate Scatter and Location

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Testing Independence in High Dimensions & Identifiability of Graphical Models

Thesis (Ph.D.)--University of Washington, 2016-06

The U.S. Gulf of Mexico Pink Shrimp, Farfantepenaeus duorarum, Fishery: 50 Years of Commercial Catch Statistics

U.S. Gulf of Mexico, pink shrimp, Farfantepenaeus duorarum, catch statistics have been collected by NOAA’s National Marine Fisheries Service, or its predecessor agency, for over 50 years. Recent events, including hurricanes and oil spills within the ecosystem of the fishery, have shown that documentation of these catch data is of primary importance. Fishing effort for this stock has fluctuated over the 50-year period analyzed, ranging from 3,376 to 31,900 days fished, with the most recent years on record, 2008 and 2009, exhibiting declines up to 90% relative to the high levels recorded in the mid 1990’s. Our quantification of F. duorarum landings and catch rates (CPUE) indicates catch have been below the long-term average of about 12 million lb for all of the last 10 years on record. In contrast to catch and effort, catch rates have increased in recent years, with record CPUE levels measured in 2008 and 2009, of 1,340 and 1,144 lb per day fished, respectively. Our regression results revealed catch was dependent upon fishing effort (F=98.48df=1, 48, p<0.001, r2=0.67), (Catch=1,623,378 + (520) × (effort)). High CPUE’s measured indicate stocks were not in decline prior to 2009, despite the decline in catch. The decrease in catch is attributed in large part to low effort levels caused by economical and not biological or habitat related conditions. Future stock assessments using these baseline data will provide further insights and management advice concerning the Gulf of Mexic

Spatial and Temporal Distribution of Sea Turtles in the Western North Atlantic and the U.S. Gulf of Mexico from Marine Recreational Fishery Statistics Survey (MRFSS)

Systematic surveys, along with opportunistic sightings, have provided important information on sea turtle (Cheloniidae and Dermochelydae) distributions, knowledge which can help reduce the risk of harmful human interaction. In 1991 and 1992, the Marine Recreational Fishery Sta- tistics Survey (MRFSS) of the National Ma- rine Fisheries Service, NOAA, provided a unique opportunity to gain additional, synoptic information on the spatial and temporal distribution of sea turtles along the U.S. Atlantic and Gulf of Mexico coasts by asking recreational anglers if they had observed a sea turtle on their fishing trip. During the spring and summer months of those years, as water temperatures warmed, the MRFSS documented an increase in sea turtle sightings in inshore waters and in a northward direction along the U.S. Atlantic Coast and in a westward direction along the northern Gulf of Mexico. This pattern reversed in the late summer and fall months as water temperatures cooled, with sea turtles concentrating along Georgia and both coasts of Florida. Although the MRFSS did not provide species or size composition of sea turtles sighted, and effort varied depending upon location of fishing activity and time of year anglers were queried, it did provide an additional and useful means of ascertaining spatial and temporal distributions of sea turtles along these coasts.

Three decades of U.S. Gulf of Mexico white shrimp, Litopenaeus setiferus, commercial catch statistics

Gulf of Mexico, white shrimp, Litopenaeus setiferus, catch statistics have been collected by NOAA’s National Marine Fisheries Service for over 50 years. Recent occurrences such as natural and manmade disasters have raised awareness for the need to publish these types of data. Here we report shrimp data collected from 1984 to 2011. These 28 years of catch history are the time series used in the most recent Gulf of Mexico white shrimp stock assessment. Fishing effort for this stock has fluctuated over the period reported, ranging from 54,675 to 162,952 days fished. Catch averaged 55.7 million pounds per year, increasing significantly over the times series. In addition, catch rates have been increasing in recent years, with CPUE levels ranging from 315 lb/day fished in 2002, to 1,175 lb/ day fished in 2008. The high CPUE’s we have measured is one indication that the stock was not in decline during this time period. Consequently, we believe the decline in effort levels is due purely to economic factors. Current stock assessments are now using these baseline data to provide managers with further insights into the Gulf L. setiferus stocks.

U.S. census of business: 1954. Central business district statistics, bulletin CBD 1-96.

Mode of access: Internet.

Study of consumer expenditures, incomes, and savings; statistical tables: Urban U. S.--1950, tabulated by the Bureau of Labor Statistics, U. S. Dept. of Labor, for the Wharton School of Finance and Commerce, University of Pennsylvania.

Mode of access: Internet.