Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Recurrence plots revisited

We demonstrate that the comparison of Tully-Fisher relations (TFRs) derived from global H I line widths to TFRs derived from the circular velocity profiles of dynamical models (or stellar kinematic observations corrected for asymmetric drift) is vulnerable to systematic and uncertain biases introduced by the different measures of rotation used. We therefore argue that to constrain the relative locations of the TFRs of spiral and S0 galaxies, the same tracer and measure must be used for both samples. Using detailed near-infrared imaging and the circular velocities of axisymmetric Jeans models of 14 nearby edge-on Sa‐Sb spirals and 14 nearby edge-on S0s drawn from a range of environments, we find that S0s lie on a TFR with the same slope as the spirals, but are on average 0:53 0:15 mag fainter at KS-band at a given rotational velocity. This is a significantly smaller offset than that measured in earlier studies of the S0 TFR, which we attribute to our elimination of the bias associated with using different rotation measures and our use of earlier type spirals as a reference. Since our measurement of the offset avoids systematic biases, it should be preferred to previous estimates. A spiral stellar population in which star formation is truncated would take 1 Gyr to fade by 0.53 mag at KS-band. If S0s are the products of a simple truncation of star formation in spirals, then this finding is difficult to reconcile with the observed evolution of the spiral/S0 fraction with redshift. Recent star formation could explain the observed lack of fading in S0s, but the offset of the S0 TFR persists as a function of both stellar and dynamical mass. We show that the offset of the S0 TFR could therefore be explained by a systematic difference between the total mass distributions of S0s and spirals, in the sense that S0s need to be smaller or more concentrated than spirals.

http://www-astro.physics.ox.ac.uk/~bureau/Publications/TFR_MNRAS10.pdf

The Tully-Fisher relations of early-type spiral and S0 galaxies

This article examines methods, issues and controversies that have arisen over the last decade in the effort to organize sequences of DNA base information into homogeneous segments. An array of different models and techniques have been considered and applied. We demonstrate that most approaches can be embedded into a suitable version of the multiple change-point problem, and we review the various methods in this light. We also propose and discuss a promising local segmentation method, namely, the application of split local polynomial fitting. The genome of bacteriophage $\lambda$ serves as an example sequence throughout the paper.

Statistical methods for DNA sequence segmentation

Determining the virial factor of the broad-line region gas is crucial for calibrating active galactic nucleus black hole mass estimators, since the measured line-of-sight velocity needs to be converted into the intrinsic virial velocity. The average virial factor has been empirically calibrated based on the M{sub BH}-{sigma}{sub *} relation of quiescent galaxies, but the claimed values differ by a factor of two in recent studies. We investigate the origin of the difference by measuring the M{sub BH}-{sigma}{sub *} relation using an updated galaxy sample from the literature and explore the dependence of the virial factor on various fitting methods. We find that the discrepancy is primarily caused by the sample selection, while the difference stemming from the various regression methods is marginal. However, we generally prefer the FITEXY and Bayesian estimators based on Monte Carlo simulations for the M{sub BH}-{sigma}{sub *} relation. In addition, the choice of independent variable in the regression leads to {approx}0.2 dex variation in the virial factor inferred from the calibration process. Based on the determined virial factor, we present the updated M{sub BH}-{sigma}{sub *} relation of local active galaxies.

https://iopscience.iop.org/article/10.1088/0067-0049/203/1/6/pdf

RECALIBRATION OF THE VIRIAL FACTOR AND M BH-σ* RELATION FOR LOCAL ACTIVE GALAXIES

This article develops statistical methods useful for comparing the marginals F and G of a bivariate distribution. Such comparisons are appropriate in the analysis of matched-pair data involving a treatment and a control (or two treatments). The quantile comparison functionq = G−1(F), proposed by Lehmann as a generalized measure of treatment effect in fully randomized experiments, is shown to be applicable and also useful in the analysis of matched-pair data. Nonparametric simultaneous confidence bands for q are constructed using asymptotic and permutation methods. The copula of the bivariate distribution plays a significant role in the methodology. Application of the results is illustrated on a dataset from an industrial experiment.

Nonparametric Confidence Bands for a Quantile Comparison Function

We consider abrupt mean-change models for data with dependent, stationary, errors. No specific distributional assumptions, other than the existence and summability of cumulants, are made. A consistency property of the least squares estimator of the change-point is derived. This leads to the construction of consistent, asymptotically normal and efficient estimators of the error spectral density function and covariances. The application of these results in testing for the existence of a change is discussed. A test for uncorrelatedness of the errors is also given. An application is made to the detection of changes in the period of a variable star. The relationship between cusum charts used in statistics and O-C diagrams used in astronomy is pointed out. 1. Introduction. In the last decade the statistical literature has seen a steady increase in the number of published results dealing with so-called change-point problems. In their simplest form these are problems concerning the detection of sudden, often discontinuous, changes in the mean of a series of observations Xi,..., Xn. To be more specific, a model of the form

/pdf/the-analysis-of-change-point-data-with-dependent-errors-fk54y899ta.pdf

The analysis of change-point data with dependent errors

Sequential rank CUSUM charts for angular data

We propose a sequential cumulative sum procedure to detect deviations from uniformity in angular data. The method is motivated by a problem in high-energy astrophysics and is illustrated by an application to data.

A cusum procedure to detect deviations from uniformity in angular data

Motivated by two applications in the mining industry, we introduce a new approach to testing the hypothesis that two-sampled distributions are simply location and scale changes of one another. The test, applicable to both paired data and two-sample data, is based on the empirical characteristic function. More conventional techniques founded on the empirical distribution function suffer from serious drawbacks when used to test for location-scale families. In the motivating applications, knowing that the distributions differ only in location and scale has significant operational and economic advantages, enabling protocols for one type of data to be applied directly to another. Supplementary material in the form of Matlab code is available online.

F. Lombard

Papers

Nonparametric Confidence Bands for a Quantile Comparison Function

The analysis of change-point data with dependent errors

Sequential rank CUSUM charts for angular data

A cusum procedure to detect deviations from uniformity in angular data

A New Approach to Function-Based Hypothesis Testing in Location-Scale Families.