Does congress realign or smoothly adjust? A discrete switching model of congressional partisan regimes

Studies of development and change in partisan fortunes in the US emphasize epochs of partisan stability, separated by critical events or turning points. In this paper we study partisan electoral changes in the US Congress using the method of Markov switching. Our estimates are based on election changes from 1854, roughly the date of the establishment of the modern incarnation of the two-party system, to the present. For the Senate, we estimate partisan balance both from 1856 and from 1914, the period of direct elections. Our discrete-state method performs better than one based on smooth cycles, and is more consistent with the existing theory.We use the Markov switching method to estimate an underlying unobserved state parameter, ‘partisan regime’. The method allows the direct estimation of critical transition points between Republican and Democratic partisan coalitions. Republican regimes characterized House elections during three periods: 1860 through 1872, 1894 through 1906, and 1918 through 1928. Senate results were roughly similar. Every recession caused a realignment prior to 1932, but since then none has.For the Senate, the two-state model does not fit adequately. We estimate a three-state model in which a Republican regime dominated from 1914 through 1928; a Democratic regime characterized the period 1930–1934, and a Democratic-leaning regime characterized the period 1938 to the present (1936 is a transition year).The driver for historical realignments up to 1930 seems to have been economic distress, at least for the House. Each recession before 1930 is associated with a realignment, but after 1930, no recession produced a realignment. Since then, however, economic downturns have not led to realignments. We speculate that better economic management since World War II, resulting in shallower recessions, is the cause. For the Senate, however, we detect only one fundamental regime shift: that during the Great Depression.     

On Integrated Volatility of Itô Semimartingales when Sampling Times are Endogenous

In this paper, we estimate the integrated volatility of Itô semimartingale when sampling times are endogenous. The estimator is proved to be consistent, and is robust to jumps, regardless of whether they are finite and infinite activity jumps. We also establish a central limit theorem for the estimator in a general endogenous time setting when the jumps have finite variation. Simulation is also included to illustrate the performance of the proposed procedure.     

Strong consistency of presmoothed Kaplan–Meier integrals when covariables are present

It is known that the Kaplan–Meier estimation may be improved via presmoothing methods. In this article, we introduce an extended presmoothed Kaplan–Meier estimator in the presence of covariates. The main result is the strong consistency of general empirical integrals based on such an estimator. As applications, one can obtain a consis-tent multivariate empirical distribution under censoring, and also can obtain a consistent estimation of regression parameters. We illustrate the new estimation methods through simulations and real data analysis.     

On the E-optimality of blocked main effects plans when n ≡ 1(mod4)

ABSTRACT

In this article, we consider experimental situations in which m two-lever factors are to be studied using a two-level main effects plan involving n runs which are partitioned into b blocks of size k =?n/b. For the casen ≡ 1(mod?4) and b???k, we derive some new methods of constructing E-optimal designs which tend to be highly efficient under other optimality criteria as well.     

Resampling estimation when observations are m–dependent

For m–dependent, identically distributed random observation, the bootstrap method provides inconsistent estimators of the distribution and variance of the sample mean. This paper proposes an alternative resampling procedure. For estimating the distribution and variance of a function of the sample mean, the proposed resampling estimators are shown to be strongly consistent.     

Moments of order statistics of Topp–Leone distribution

We derive explicit algebraic expressions for both of the single and product moments of order statistics from Topp–Leone distribution. We also give an identity about single moments of order statistics. These expressions will be useful for computational purposes.     

Estimating means when sampling gives probabilities as well as values or “Looking a gift horse in the mouth”

Consider the random sampling of a discrete population. The observations, as they are collected one by one, are enhanced in that the probability mass associated with each observation is also observed. The goal is to estimate the population mean. Without this extra information about probability mass, the best general purpose estimator is the arithmetic average of the observations, XBAR. The issue is whether or not the extra information can be used to improve on XBAR. This paper examines the issues and offers four new estimators, each with its own strengths and liabilities. Some comparative performances of the four with XBAR are made.The motivating application is a Monte Carlo simulation that proceeds in two stages. The first stage independently samples n characteristics to obtain a configuration of some kind, together with a configuration probability p obtained, if desired, as a product of n individual probabilities. A relatively expensive calculation then determines an output X as a function of the configuration. A random sample of X could simply be averaged to estimate the mean output, but there are possibly more efficient estimators on account of the known configuration probabilities.     

Characteristics of some classes of space–time covariance functions

Although a wide list of classes of space–time covariance functions is now available, selecting an appropriate class of models for a variable under study is still difficult and it represents a priority problem with respect to the choice of a particular model of a specified class. Then, knowing the characteristics of various classes of covariances, and their auxiliary functions, and matching those with the characteristics of the empirical space–time covariance surface might be helpful in the selection of a suitable class. In this paper some characteristics, such as behavior at the origin, asymptotic behavior, nonseparability and anisotropy aspects, are studied for some well known classes of covariance models of stationary space–time random fields. Moreover, some important issues related to modeling choices are described and a case study is presented.     

Segmentation of the mean of heteroscedastic data via cross-validation

This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. A new family of change-point detection procedures is proposed, showing that cross-validation methods can be successful in the heteroscedastic framework, whereas most existing procedures are not robust to heteroscedasticity. The robustness to heteroscedasticity of the proposed procedures is supported by an extensive simulation study, together with recent partial theoretical results. An application to Comparative Genomic Hybridization (CGH) data is provided, showing that robustness to heteroscedasticity can indeed be required for their analysis.     

On ℓ-overlapping Runs of Ones of Length k in Sequences of Independent Binary Random Variables

Consider a finite sequence of independent binary (zero-one) random variables ordered on a line or on a circle. The number of the ?-overlapping runs of ones of a fixed length k is studied for both types of the concerned ordering. Recurrences for the exact probability mass functions for these numbers are obtained via simple probabilistic arguments. Exact closed formulae, for the mean and variance of the studied numbers are obtained via their representations through properly defined indicators. Two application case studies, concerning record sequences and reliability of consecutive systems, clarify further the theoretical results.     

Equivalent Conditions of Complete Moment Convergence of Weighted Sums for ϕ-Mixing Sequence of Random Variables

In this article, the complete moment convergence of weighted sums for ?-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for ?-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li et al. (1995 Li, D.L., Rao, M.B., Jiang, T.F., Wang, X.C. (1995). Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8:49–76.[Crossref], [Web of Science ®] , [Google Scholar]) and Gut (1993 Gut, A. (1993). Complete convergence and Cesàro summation for i.i.d. random variables. Probab. Theory Related Fields 97:169–178.[Crossref], [Web of Science ®] , [Google Scholar]) from i.i.d. to ?-mixing setting. Moreover, we obtain the complete moment convergence of moving average processes based on ?-mixing random variables, which extends the result of Kim et al. (2008 Kim, T.S., Ko, M.H. (2008). Complete moment convergence of moving average processes under dependence assumptions. Statist. Probab. Lett. 78:839–846.[Crossref], [Web of Science ®] , [Google Scholar]) in the sense that it does not require a specific mixing rate.     

Estimation of the Parameters of the Birnbaum–Saunders Distribution

Some alternative estimators to the maximum likelihood estimators of the two parameters of the Birnbaum–Saunders distribution are proposed. Most have high efficiencies as measured by root mean square error and are robust to departure from the model as well as to outliers. In addition, the proposed estimators are easy to compute. Both complete and right-censored data are discussed. Simulation studies are provided to compare the performance of the estimators.     

Evaluation of Measurement Comparisons Using Generalized Least Squares: the Role of Participants’ Estimates of Systematic Error

We consider the evaluation of laboratory practice through the comparison of measurements made by participating metrology laboratories when the measurement procedures are considered to have both fixed effects (the residual error due to unrecognised sources of error) and random effects (drawn from a distribution of known variance after correction for all known systematic errors). We show that, when estimating the participant fixed effects, the random effects described can be ignored. We also derive the adjustment to the variance estimates of the participant fixed effects due to these random effects.     

The Effect of Verification Bias in the Naïve Estimators of Accuracy of a Binary Diagnostic Test

The assessment of a binary diagnostic test requires a knowledge of the disease status of all the patients in the sample through the application of a gold standard. In practice, the gold standard is not always applied to all of the patients, which leads to the problem of partial verification of the disease. When the accuracy of the diagnostic test is assessed using only those patients whose disease status has been verified using the gold standard, the estimators obtained in this way, known as Naïve estimators, may be biased. In this study, we obtain the explicit expressions of the bias of the Naïve estimators of sensitivity and specificity of a binary diagnostic test. We also carry out simulation experiments in order to study the effect of the verification probabilities on the Naïve estimators of sensitivity and specificity.     

Statistical choice of extreme value domains of attraction — a comparative analysis

In recent years there has been a significant development of several procedures to infer about the extremal model that most conveniently describes the distribution function of the underlying population from a data set. The problem of choosing one of the three extremal types, giving preference to the Gumbel model for the null hypothesis, has frequently received the general designation of statistical choice of extremal models and has been handled under different set-ups by numerous authors. Recently, a test procedure, referred by Hasofer and Wang (1992), gave place to a comparison with some of other connected perspectives. Such a topic, jointly with some suggestions for applicability to real data, is the theme of the present paper.     

Reliability characteristics of Farlie–Gumbel–Morgenstern family of bivariate distributions

Abstract

In this paper, we study the Farlie–Gumbel–Morgenstern family of bivariate distributions from a reliability point of view. The properties of this family of distributions and the association between the two variables are investigated by studying the local dependence function and the association measure defined by Clayton (1978 Clayton, D.G. (1978). A model for association in bivariate life tables and its applications in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151.[Crossref], [Web of Science ®] , [Google Scholar]). We also study the effect of the association parameter on the hazard components, the failure rate of the series system, and the regression mean residual life of a parallel system. Stochastic comparisons with respect to the association parameter are also studied. Some examples are provided to illustrate the results.