Paul I. Nelson

Quasi-likelihood estimation for semimartingales

A technique of parameter estimation for a semimartingale based on the maximization of a likelihood type function is proposed. This technique is shown to be optimal in the sense of Godambe within a certain class of estimating equations. The resulting estimators are shown to be consistent and asymptotically normally distributed on certain events under relatively weak assumptions.

Some properties of Kendall's partial rank correlation coefficient

We show through a simulation study that the approximate distribution of Kendalls partial rank correlation coefficient [tau]12.3 can be obtained by Jackknifing. We also present some examples which demonstrate that [tau]12.3 can be difficult to interpret.

Prediction of Gamma failure times

Statistically-independent operating components, each of which follows a Gamma failure-law, are simultaneously put into service. Two predictors of later failure times, based on observations of earlier failures, are proposed and investigated. The predictors are in the form of estimated conditional mean and median of the value being predicted. Unknown parameters of the underlying failure law are estimated by the method of maximum likelihood (ML), and the predictors are constructed using a parametric bootstrap. These conditional median and mean predictors provide a relatively easy method to compute predictors of future Gamma order statistics. Simulation indicates that these predictors are effective except when the shape parameter of the Gamma distribution is small. Generally, the larger the fraction of available data and the closer the value being predicted, the more accurate the predictions (as anticipated). The simulation also detected some difficulty in implementing ML for the gamma based on type-II censored data when the sample ratio of the geometric mean to the arithmetic mean is very close to 1. This problem warrants further study.

Short-term temporal stability of interpersonal attraction

The temporal stability of attitude-evoked attraction responses and the similarity-attraction relationship were examined across a 1-week time interval In the absence of additional information concerning a stranger, attraction toward the stranger was found to be highly stable (p <.001). In addition, the positive relationship between similarity and attraction was found to be quite stable (p <. 01) across this time period.

A note on estimating a non-increasing density in the presence of selection bias

Abstract In this paper we construct the non-parametric maximum likelihood estimator (NPMLE) f n of a non-increasing probability density function f with distribution function F on the basis of a sample from a weighted distribution G with density given by g(x)=w(x)f(x)/μ(f,w), where w(u)>0 for all u and μ(f,w)=∫w(u)f(u) d u is the normalizing constant. We show that the NPMLE of f is proportional to the Grenander (Skand. Akt. 39 (1956) 125) estimator of the density of transformed data using a simple transformation based on w. We explore some of the properties of f n and show that the Prakasa Rao Theorem (Sankhya A 31 (1969) 23) extends to the weighted case. We also give conditions under which the resulting distribution function F n is strongly uniformly consistent and show that a rate of convergence of order n−1/2 can be achieved under conditions on w. We also investigate estimation of f when a second sample directly from f is available and carry out a small-scale simulation study of the performance of two estimators in this case.

An asymptotically distribution freetest for assessing the separationbetween two distributions

We present a class of asymptotically distribution free tests for the equality of selected quantiles of two continuous distributions F and G based on independent random samples summarized by their empirical distribution functions, denoted [Fcirc] and Ĝ. Our test statistics are based on [Fcirc] evaluated at a quantile of the distribution function H defined as the weighted average Ĥ = b[Fcirc] + (l - b)Ĝ, 0≤b<1. The choice b = 0 yields the control quantile test studied by Chakraborti [4] and others. Inversion of the test statistic defined by b = 0.5 leads to a measure of the separation between F and G. We investigate and compare the performance of some of these tests and a normal theory test proposed by Perng et al. [12] via simulation.

Testing for a separation between two normal distributions

Three tests are proposed for testing for a specified degree of overlap between two normal distributions, The hypotheses considered are an extension of the Behrens-Fisher problem, A simulation study of the performance of the tests is presented.

An omnibus lack of fit test in logistic regression with sparse data

The usefulness of logistic regression depends to a great extent on the correct specification of the relation between a binary response and characteristics of the unit on which the response is recoded. Currently used methods for testing for misspecification (lack of fit) of a proposed logistic regression model do not perform well when a data set contains almost as many distinct covariate vectors as experimental units, a condition referred to as sparsity. A new algorithm for grouping sparse data to create pseudo replicates and using them to test for lack of fit is developed. A simulation study illustrates settings in which the new test is superior to existing ones. Analysis of a dataset consisting of the ages of menarche of Warsaw girls is also used to compare the new and existing lack of fit tests.

A Study of Effectiveness of Thin Surface Treatments Using Hamburg Wheel Tracking Device

In recent years, more and more highway agencies are adopting preventive maintenance strategies or thin surface treatments to bring pavements back to appropriate serviceability for road users. This paper discusses the effectiveness of several thin surface or preventive maintenance treatments on sixteen highway test sections in Kansas. The treatments studied include thin Hot-Mix Asphalt (HMA) overlay, ultra-thin bonded asphalt surface (Nova Chip), and chip seal. These treatments were applied with three different types of surface preparation- bare surface, 1” surface recycle (hot in-place recycling), and 2” surface recycle. Hamburg Wheel-Tracking Device (HWTD) test was conducted on the cores from the test sections with thin surface treatments under this study. The laboratory test results show that most projects exceeded the maximum rut depth limit (20 mm) specified in the study and the number of wheel passes to failure varied significantly among the projects. Cores from only three projects, two treated with Nova Chip and one with 1” HMA overlay, carried 20,000 wheel passes without exceeding maximum rut depth limit. Pair-wise comparisons or contrasts among the treatments were performed with the statistical analysis software, SAS. Air void of the HWTD test cores was found to be a significant factor affecting the performance of thin surface treatments. Since the Hamburg test samples (62 mm tall) consisted mostly of underlying layer materials, it was concluded that quality of this layer is the major determinant of performance of pavements with thin surface treatments.

Nonparametric tests for the median from a size-biased sample

Abstract This study explores issues related to one-sample nonparametric tests for the median of a continuous distribution when the sample is collected via size-bias of a known order. A general principle on how to construct the reference distribution of a given test statistic is presented. Following this principle, we create new bias-corrected nonparametric testing procedures. Computationally intensive, exact P-values are available for a small sample. When the sample size is large, P-values can be easily estimated by the asymptotic approximation developed here. Power functions of these tests are investigated in both small- and large-sample cases and consistency is shown to hold under fairly general conditions. The tests’ performances are then compared via asymptotic relative efficiency under four theoretical distributions.