Semiparametric Sieve-Type Generalized Least Squares Inference

This article considers the problem of statistical inference in linear regression models with dependent errors. A sieve-type generalized least squares (GLS) procedure is proposed based on an autoregressive approximation to the generating mechanism of the errors. The asymptotic properties of the sieve-type GLS estimator are established under general conditions, including mixingale-type conditions as well as conditions which allow for long-range dependence in the stochastic regressors and/or the errors. A Monte Carlo study examines the finite-sample properties of the method for testing regression hypotheses.     

Three-stage and ‘accelerated’ sequential procedures for the mean of a normal population with known coefficient of variation

Three-stage and ‘accelerated’ sequential procedures are developed for estimating the mean of a normal population when the population coefficient of variation (CV) is known. In spite of the usual estimator, i.e. the sample mean, Searls' (1964 Searls, DT. (1964). The utilization of a known coefficient of variation in the estimation procedure. J. Amer. Statist. Assoc, 50: 1225–1226.  ) estimator is utilized for the estimation purpose. It is established that Searls' estimator dominates the sample mean under the two sampling schemes.     

LAW ENFORCEMENT AND WRONGFUL ARRESTS WITH ENDOGENOUSLY (IN)COMPETENT OFFICERS

Economic intuition suggests that enforcement errors incentivize crimes, therefore officers must be penalized for committing such errors. Legal scholars argue that if penalties for errors are severe, officers may become timid while policing (thereby encouraging crime). We evaluate these arguments in a model where officers invest in competence. Competence increases the officer's ability to identify criminals. Low sanctions for errors encourages bold policing by officers but may still raise the equilibrium level of crime because it also discourages investments in competence. Granting immunity to only competent officers (“qualified immunity”) reduces both errors and crimes when competence is observable. (JEL K4, K42, L5)     

On measuring vulnerability to poverty

There is a growing interest on dynamic and broader concepts of deprivation such as vulnerability, which takes in to account the destitution of individuals from future shocks. We use the framework of decision making under uncertainty to arrive at a new measure of vulnerability to poverty. We highlight the importance of current standard of living to better capture the notion of vulnerability. In conceptualizing the new class of measures of vulnerability, we thus move beyond the standard expected poverty measures that is commonly found in the literature. We also axiomatically characterize the new class of measure and discuss some of its properties.     

Bootstrap-assisted tests of symmetry for dependent data*

The paper considers the problem of testing for symmetry (about an unknown centre) of the marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using the autoregressive sieve bootstrap and stationary bootstrap procedures to obtain critical values and P-values for symmetry tests is explored. Bootstrap-assisted tests for symmetry are straightforward to implement and require no prior estimation of asymptotic variances. The small-sample properties of a wide variety of tests are investigated using Monte Carlo experiments. A bootstrap-assisted version of the triples test is found to have the best overall performance.     

Robust Bayesian analysis of generalized inverted family of distributions

ABSTRACT

In the current study we develop the robust Bayesian inference for the generalized inverted family of distributions (GIFD) under an ε-contamination class of prior distributions for the shape parameter α, with different possibilities of known and unknown scale parameter. We used Type II censoring and Bartholomew sampling scheme (1963) for the following derivations under the squared-error loss function (SELF) and linear exponential (LINEX) loss function : ML-II Bayes estimators of the i) parameters; ii) Reliability function and; iii) Hazard function. We also present simulation study and analysis of a real data set.     

Corrections and amendments

In the Competing risk analysis g_i(t) the failure rates h_i(t) and g_i(t) (as defined ) are, in general, not the same. However, of the survival times due to different causes are independent, then g_i (t) = h_i (t) this is a model studied by chiang (1961). In this note we have exhibited some counterexamples illustrating the relationships between g_i (t)= h_i (t) and the independence of survival times.     

Balanced Treatment incomplete block (BTIB) designs for comparing treatments with a control: minimal complete sets of generator designs for k = 3, p = 3(1)10

Bechhofer and Tamhane (1981) proposed a new class of incomplete block designs called BTIB designs for comparing p ≥ 2 test treatments with a control treatment in blocks of equal size k < p + 1. All BTIB designs for given (p,k) can be constructed by forming unions of replications of a set of elementary BTIB designs called generator designs for that (p,k). In general, there are many generator designs for given (p,k) but only a small subset (called the minimal complete set) of these suffices to obtain all admissible BTIB designs (except possibly any equivalent ones). Determination of the minimal complete set of generator designs for given (p,k) was stated as an open problem in Bechhofer and Tamhane (1981). In this paper we solve this problem for k = 3. More specifically, we give the minimal complete sets of generator designs for k = 3, p = 3(1)10; the relevant proofs are given only for the cases p = 3(1)6. Some additional combinatorial results concerning BTIB designs are also given.     

Appointment Scheduling with No‐Shows and Overbooking

We study an overbooking model for scheduling arrivals at a medical facility under no‐show behavior, with patients having different no‐show probabilities and different weights. The scheduler has to assign the patients to time slots in such a way that she minimizes the expected weighted sum of the patients' waiting times and the doctor's idle time and overtime. We first consider the static problem, where the set of patients to be scheduled and their characteristics are known in advance. We partially characterize the optimal schedule and introduce a new sequencing rule that schedules patients according to a single index that is a function of their characteristics. Then we apply our theoretical results and conclusions from numerical experiments to sequential scheduling procedures. We propose a heuristic solution to the sequential scheduling problem, where requests for appointments come in gradually over time and the scheduler has to assign each patient to one of the remaining slots that are available in the schedule for a given day. We find that the no‐show rate and patients' heterogeneity have a significant impact on the optimal schedule and should be taken under consideration.