Regression with outlier shrinkage

We propose a robust regression method called regression with outlier shrinkage (ROS) for the traditional n>p$n>p$ cases. It improves over the other robust regression methods such as least trimmed squares (LTS) in the sense that it can achieve maximum breakdown value and full asymptotic efficiency simultaneously. Moreover, its computational complexity is no more than that of LTS. We also propose a sparse estimator, called sparse regression with outlier shrinkage (SROS), for robust variable selection and estimation. It is proven that SROS can not only give consistent selection but also estimate the nonzero coefficients with full asymptotic efficiency under the normal model. In addition, we introduce a concept of nearly regression equivariant estimator for understanding the breakdown properties of sparse estimators, and prove that SROS achieves the maximum breakdown value of nearly regression equivariant estimators. Numerical examples are presented to illustrate our methods.     

Do Leading Indicators Lead Peaks More Than Troughs?

We develop a novel Markov switching vector autoregressive model to investigate the possibility that leading indicators have different lead times at business cycle peaks and at troughs. In this model, coincident and leading indicators share a common Markov state process, but their cycles are nonsynchronous, with the nonsynchronicity varying across regimes. An application shows that on average the Conference Board’s Composite Leading Index leads the Composite Coincident Index by nearly 1 year at peaks but by only 1 quarter at troughs. Allowing for asymmetric lead times yields improved real-time dating and forecasting of business cycle turning points.     

Combination of Economic Forecasts: An Odds-Matrix Approach

In this article, we test a new method of combining economic forecasts, the odds-matrix approach, using Clemen and Winkler's (1986) data on gross-national-product forecasts. For these data, the results show that the odds-matrix method is more accurate than each of the other methods tested and can be expected to be especially useful when data are nonstationary or sparse.     

Bayesian and Frequentist Inference in Partially Identified Models

A large‐sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by an identifiable finite‐dimensional reduced‐form parameter vector. It is used to analyze the differences between Bayesian credible sets and frequentist confidence sets. We define a plug‐in estimator of the identified set and show that asymptotically Bayesian highest‐posterior‐density sets exclude parts of the estimated identified set, whereas it is well known that frequentist confidence sets extend beyond the boundaries of the estimated identified set. We recommend reporting estimates of the identified set and information about the conditional prior along with Bayesian credible sets. A numerical illustration for a two‐player entry game is provided.     

Inference for longitudinal data from complex sampling surveys: An approach based on quadratic inference functions

We propose a survey weighted quadratic inference function method for the analysis of data collected from longitudinal surveys, as an alternative to the survey weighted generalized estimating equation method. The procedure yields estimators of model parameters, which are shown to be consistent and have a limiting normal distribution. Furthermore, based on the inference function, a pseudolikelihood ratio type statistic for testing a composite hypothesis on model parameters and a statistic for testing the goodness of fit of the assumed model are proposed. We establish their asymptotic distributions as weighted sums of independent chi‐squared random variables and obtain Rao‐Scott corrections to those statistics leading to a chi‐squared distribution, approximately. We examine the performance of the proposed methods in a simulation study.     

A shift-dependent generalized cumulative entropy of order n

Recently, a shift-independent information measure known as generalized cumulative entropy of order n (GCE_n) was proposed by Kayal (2016 Kayal, S. 2016. On generalized cumulative entropies. Probability in Engineering and Informational Sciences 30:640–62. [Google Scholar]). In this communication, we propose a shift-dependent version of GCE_n. Various properties including the effect of transformations, bounds etc. have been discussed. Several relationships of the shift-dependent GCE_n with some well-known reliability measures are studied. Few characterization results are obtained. We derive an estimator for the proposed measure via empirical distribution function approach. Large sample properties of the estimator are studied when independent observations are taken from a Weibull distribution.     

A New lifetime model for multivariate survival data with a surviving fraction

In this paper we propose a new lifetime model for multivariate survival data with a surviving fraction. We develop this model assuming that there are m types of unobservable competing risks, where each risk is related to a time of the occurrence of an event of interest. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. We also perform a simulation study in order to analyse the frequentist coverage probabilities of credible interval derived from posteriors. Our modelling is illustrated through a real data set.     

Nonparametric predictive inference for diagnostic test thresholds

Abstract

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning and credit scoring. The receiver operating characteristic (ROC) curve and surface are useful tools to assess the ability of diagnostic tests to discriminate between ordered classes or groups. To define these diagnostic tests, selecting the optimal thresholds that maximize the accuracy of these tests is required. One procedure that is commonly used to find the optimal thresholds is by maximizing what is known as Youden’s index. This article presents nonparametric predictive inference (NPI) for selecting the optimal thresholds of a diagnostic test. NPI is a frequentist statistical method that is explicitly aimed at using few modeling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. Based on multiple future observations, the NPI approach is presented for selecting the optimal thresholds for two-group and three-group scenarios. In addition, a pairwise approach has also been presented for the three-group scenario. The article ends with an example to illustrate the proposed methods and a simulation study of the predictive performance of the proposed methods along with some classical methods such as Youden index. The NPI-based methods show some interesting results that overcome some of the issues concerning the predictive performance of Youden’s index.     

A Stochastic Volatility Model With Realized Measures for Option Pricing

Abstract

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options.     

Generalized exponential distribution: different method of estimations

Recently a new distribution, named as generalized exponential distribution has been introduced and studied quite extensively by the authors. Generalized exponential distribution can be used as an alternative to gamma or Weibull distribution in many situations. In a companion paper, the authors considered the maximum likelihood estimation of the different parameters of a generalized exponential distribution and discussed some of the testing of hypothesis problems. In this paper we mainly consider five other estimation procedures and compare their performances through numerical simulations.