Stochastic metafrontiers

ABSTRACT

We consider the case of production units arranged into a number of groups. All units within a group choose output–input combinations from the same production possibilities set that is represented by a stochastic frontier model. The metafrontier is the envelope of the group-specific frontiers. We are interested in the metafrontier distance, which is the amount by which the group-specific frontier lies below the metafrontier.

Previous work has measured the metafrontier distance using the deterministic portion of the frontier. In a stochastic frontier model, this is not appropriate. We show how to evaluate the metafrontier distance, and we demonstrate the empirical relevance of this issue.     

New sensitivity analysis subordinated to a contrast

ABSTRACT

In a model of the form Y = h(X₁, …, X_d) where the goal is to estimate a parameter of the probability distribution of Y, we define new sensitivity indices which quantify the importance of each variable X_i with respect to this parameter of interest. The aim of this paper is to define goal oriented sensitivity indices and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution Y. We name the framework we present as Goal Oriented Sensitivity Analysis (GOSA).     

Corrected likelihood ratio and score tests for the beta distribution

We present correction formulae to improve likelihood ratio and score teats for testing simple and composite hypotheses on the parameters of the beta distribution. As a special case of our results we obtain improved tests for the hypothesis that a sample is drawn from a uniform distribution on (0, 1). We present some Monte Carlo investigations to show that both corrected tests have better performances than the classical likelihood ratio and score tests at least for small sample sizes.     

An Introduction to Second-Generation p-Values

ABSTRACT

Second generation p-values preserve the simplicity that has made p-values popular while resolving critical flaws that promote misinterpretation of data, distraction by trivial effects, and unreproducible assessments of data. The second-generation p-value (SGPV) is an extension that formally accounts for scientific relevance by using a composite null hypothesis that captures null and scientifically trivial effects. Because the majority of spurious findings are small effects that are technically nonnull but practically indistinguishable from the null, the second-generation approach greatly reduces the likelihood of a false discovery. SGPVs promote transparency, rigor and reproducibility of scientific results by a priori identifying which candidate hypotheses are practically meaningful and by providing a more reliable statistical summary of when the data are compatible with the candidate hypotheses or null hypotheses, or when the data are inconclusive. We illustrate the importance of these advances using a dataset of 247,000 single-nucleotide polymorphisms, i.e., genetic markers that are potentially associated with prostate cancer.     

Residual analysis for unidimensional scaling in the L2-norm

ABSTRACT

We present a procedure (RAUS) for residual analysis of a dissimilarity matrix whereby unidimensional scaling is successively applied to the absolute value of residuals. A key advantage of RAUS is that the efficient Defays formulation of unidimensional scaling can be used for the fitting of each scale. An example using U.S. Supreme Court voting data is provided to illustrate the interpretation of successive scales. A simulation study was performed to evaluate RAUS.     

Generalized spatial regression with differential regularization

ABSTRACT

We aim at analysing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, OR, USA.     

A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS

ABSTRACT

We propose a new semiparametric Weibull cure rate model for fitting nonlinear effects of explanatory variables on the mean, scale and cure rate parameters. The regression model is based on the generalized additive models for location, scale and shape, for which any or all distribution parameters can be modeled as parametric linear and/or nonparametric smooth functions of explanatory variables. We present methods to select additive terms, model estimation and validation, where all computational codes are presented in a simple way such that any R user can fit the new model. Biases of the parameter estimates caused by models specified erroneously are investigated through Monte Carlo simulations. We illustrate the usefulness of the new model by means of two applications to real data. We provide computational codes to fit the new regression model in the R software.     

The New Statistics for Better Science: Ask How Much,How Uncertain,and What Else Is Known

Abstract

The “New Statistics” emphasizes effect sizes, confidence intervals, meta-analysis, and the use of Open Science practices. We present three specific ways in which a New Statistics approach can help improve scientific practice: by reducing overconfidence in small samples, by reducing confirmation bias, and by fostering more cautious judgments of consistency. We illustrate these points through consideration of the literature on oxytocin and human trust, a research area that typifies some of the endemic problems that arise with poor statistical practice.     

General linear estimators under the prediction error sum of squares criterion in a linear regression model

In this paper, the notion of the general linear estimator and its modified version are introduced using the singular value decomposition theorem in the linear regression model y=X β+e to improve some classical linear estimators. The optimal selections of the biasing parameters involved are theoretically given under the prediction error sum of squares criterion. A numerical example and a simulation study are finally conducted to illustrate the superiority of the proposed estimators.     

ON THE EVALUATION OF CONTROL CHART LIMITS BASED ON PREDICTIVE DISTRIBUTIONS

ABSTRACT

We propose a Bayesian approach to obtaining control charts when there is parameter uncertainty. Our approach consists of two stages, (i) construction of the control chart where we use a predictive distribution based on a Bayesian approach to derive the rejection region, and (ii) evaluation of the control chart where we use a sampling theory approach to examine the performance of the control chart under various hypothetical specifications for the data generation model.     

Perturbation analysis of Markov modulated fluid models

ABSTRACT

We consider perturbations of positive recurrent Markov modulated fluid models. In addition to the infinitesimal generator of the phases, we also perturb the rate matrix, and analyze the effect of those perturbations on the matrix of first return probabilities to the initial level. Our main contribution is the construction of a substitute for the matrix of first return probabilities, which enables us to analyze the effect of the perturbation under consideration.     

The exponentiated-log-logistic geometric distribution: Dual activation

ABSTRACT

The log-logistic distribution is commonly used to model lifetime data. We propose a wider distribution, named the exponentiated log-logistic geometric distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic geometric distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.     

An algorithm for the Buckley–James estimator with interval-censored data

The Buckley–James estimator (BJE) [J. Buckley and I. James, Linear regression with censored data, Biometrika 66 (1979), pp. 429–436] has been extended from right-censored (RC) data to interval-censored (IC) data by Rabinowitz et al. [D. Rabinowitz, A. Tsiatis, and J. Aragon, Regression with interval-censored data, Biometrika 82 (1995), pp. 501–513]. The BJE is defined to be a zero-crossing of a modified score function H(b), a point at which H(·) changes its sign. We discuss several approaches (for finding a BJE with IC data) which are extensions of the existing algorithms for RC data. However, these extensions may not be appropriate for some data, in particular, they are not appropriate for a cancer data set that we are analysing. In this note, we present a feasible iterative algorithm for obtaining a BJE. We apply the method to our data.     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.     

Semiparametric estimator for a secondary analysis with correlated outcomes

ABSTRACT

Researchers are often required to reuse data that have been collected and analyzed for other purposes. Issues may arise if the outcome of this secondary study is related to the outcome of the first study and traditional methods may fail to deliver a consistent estimate. Here we propose a semiparametric approach that takes this correlation into account and produces asymptotically consistent and normally distributed estimates. We discuss its performance through simulations and apply the proposed method to a real dataset.     

Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary

ABSTRACT

Recent efforts by the American Statistical Association to improve statistical practice, especially in countering the misuse and abuse of null hypothesis significance testing (NHST) and p-values, are to be welcomed. But will they be successful? The present study offers compelling evidence that this will be an extraordinarily difficult task. Dramatic citation-count data on 25 articles and books severely critical of NHST's negative impact on good science, underlining that this issue was/is well known, did nothing to stem its usage over the period 1960–2007. On the contrary, employment of NHST increased during this time. To be successful in this endeavor, as well as restoring the relevance of the statistics profession to the scientific community in the 21st century, the ASA must be prepared to dispense detailed advice. This includes specifying those situations, if they can be identified, in which the p-value plays a clearly valuable role in data analysis and interpretation. The ASA might also consider a statement that recommends abandoning the use of p-values.     

Bayesian hypothesis testing for selected regression coefficients

ABSTRACT

We develop new Bayesian regression tests for prespecified regression coefficients. Simple, closed forms of the Bayes factors are derived that depend only on the regression t-statistic and F-statistic and the usual associated t and F distributions. The priors that allow those forms are simple and also meaningful, requiring minimal but practically important subjective inputs.     

On the relevance of weaker instruments

ABSTRACT

We study the asymptotic properties of the standard GMM estimator when additional moment restrictions, weaker than the original ones, are available. We provide conditions under which these additional weaker restrictions improve the efficiency of the GMM estimator. To detect “spurious” identification that may come from invalid moments, we rely on the Hansen J-test that assesses the compatibility between existing restrictions and additional ones. Our simulations reveal that the J-test has good power properties and that its power increases with the weakness of the additional restrictions. Our theoretical characterization of the J-test provides some intuition for why that is.     

Functionals of Markovian Branching D-BMAPS

Abstract

We consider a stochastic system in which Markovian customer attribute processes are initiated at customer arrivals in a discrete batch Markovian arrival process (D-BMAP). We call the aggregate a Markovian branching D-BMAP. Each customer attribute process is an absorbing discrete time Markov chain whose parameters depend both on the phase transition, of the driving D-BMAP, and the number of arrivals taking place at the customer's arrival instant. We investigate functionals of Markovian branching D-BMAPs that may be interpreted as cumulative rewards collected over time for the various customers that arrive to the system, in the transient and asymptotic cases. This is achieved through the derivation of recurrence relations for expected values and Laplace transforms in the former case, and Little's law in the latter case.