Weak Identification in Fuzzy Regression Discontinuity Designs

In fuzzy regression discontinuity (FRD) designs, the treatment effect is identified through a discontinuity in the conditional probability of treatment assignment. We show that when identification is weak (i.e., when the discontinuity is of a small magnitude), the usual t-test based on the FRD estimator and its standard error suffers from asymptotic size distortions as in a standard instrumental variables setting. This problem can be especially severe in the FRD setting since only observations close to the discontinuity are useful for estimating the treatment effect. To eliminate those size distortions, we propose a modified t-statistic that uses a null-restricted version of the standard error of the FRD estimator. Simple and asymptotically valid confidence sets for the treatment effect can be also constructed using this null-restricted standard error. An extension to testing for constancy of the regression discontinuity effect across covariates is also discussed. Supplementary materials for this article are available online.     

Recurrence relations for the moments of order statistics from a beta distribution

Certain recurrence relations for the single and product moments of the order statistics of a random sample of sizen arising from a beta distribution are derived. The usefulness of these relations in evaluating the single and product moments of beta order statistics is also discussed.     

On a generalization to Marshall–Olkin scheme and its application to Burr type XII distribution

Marshall–Olkin semi-Burr and Marshall–Olkin Burr distributions are introduced and studied. Their various characteristics in reliability analysis are derived. Applications in time series analysis are discussed.     

Concomitant record ranked set sampling

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.     

Markov-switching generalized additive models

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate.     

New simulation results for the calibration and inverse median estimation problems

This paper gives the results of a new simulation study for the familiar calibration problem and the less familiar inverse median estimation problem. The latter arises when one wishes to estimate from a linear regression analysis the value of the independent variable corresponding to a specified value of the median of the dependent variable. For example, from the results of a regression analysis between stress and time to failure, one might wish to estimate the stress at which the median time to failure is 10,000 hours. In the study, the mean square error, Pitman closeness, and probability of overestimation are compared for both the calibration problem and the inverse median estimation problem for (1) the classical estimator, (2) the inverse estimator, and (3) a modified version of an estimator proposed by Naszodi (1978) for both a small sample and a moderately large sample situation.     

A Novel Asymmetric Distribution with Power Tails

In this article, we propose a four-parameter asymmetric doubly Pareto-uniform (DPU) distribution with support (?∞, ∞) whose density and cumulative distribution functions are constructed by seamlessly concatenating the left and right Pareto tails with a uniform central part. Properties of the distribution are described and a maximum likelihood estimation (MLE) procedure for its parameters is obtained. Two illustrative examples of the MLE procedure are provided. The first example utilizes an i.i.d. sample of standardized log-differences of bi-monthly 30-year U.S. conventional mortgage interest rates (1971–2004). The second example deals with the height of 100 female Australian athletes.     

a study of the generalized tukey lambda family

The Tukey lambda family of distributions together with its extensions have played an important role in statistical practice. In this paper a con¬tinuously defined two-parameter generalization of this family, which holds promise of a variety of additional applications, is variously studied. The coefficients of skewness and kurtosis and the density shapes of its members are examined and the family is related to the classical Pearsonian system of distributions.     

Health of Carers of Young People with Early Psychosis: A Biopsychosocial Approach

Despite widespread recognition of the usefulness of a biopsychosocial approach in social work, there are limited studies exploring how social workers can use this approach to support the health and wellbeing of carers of young people with first episode psychosis (FEP). Validated questionnaires and anthropometric measures were used to assess the physical health and wellbeing of 42 carers of young people with FEP. Carers had moderate levels of negative caregiving consequences, quality of life, and health status. More than half (52.4%) of carers were experiencing social isolation. Many carers were overweight (78.6%), had a high risk for type 2 diabetes (39.0%), and had hypertension (33.3%). Practical implications of a biopsychosocial approach to social work that supports both clients and their carers are discussed.