A discrete/continuous choice model on a nonconvex budget set

Decreasing block rate pricing is a nonlinear price system often used for public utility services. Residential gas services in Japan and the United Kingdom are provided under this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which has not been examined in previous studies, arises because a consumer’s budget set (a set of affordable consumption amounts) is nonconvex, and hence, the resulting model includes highly nonlinear functions. To address this problem, we propose a feasible, efficient method of demand estimation on the nonconvex budget. The advantages of our method are as follows: (i) the construction of an Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite–Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.     

Selected singular-generalized-hyperbolic distributions with applications to order statistics and reliability

In this paper, the truncated version of the selected multivariate generalized-hyperbolic distributions is introduced. Considering special truncations, the joint distribution of the consecutive order statistics from the multivariate generalized-hyperbolic (GH) distribution is derived. It is shown that this joint distribution can be expressed as mixtures of the truncated selected-GH distributions. All of these truncated distributions are expressed as the selected singular-GH distributions. These results are used to obtain some expressions for the reliability measures such as mean residual life time, mean inactivity time and regression mean residual life for k-out-of-n systems.     

Goodness-of-fit tests for binomial AR(1) processes

The binomial AR(1) model describes a nonlinear process with a first-order autoregressive (AR(1)) structure and a binomial marginal distribution. To develop goodness-of-fit tests for the binomial AR(1) model, we investigate the observed marginal distribution of the binomial AR(1) process, and we tackle its autocorrelation structure. Motivated by the family of power-divergence statistics for handling discrete multivariate data, we derive the asymptotic distribution of certain categorized power-divergence statistics for the case of a binomial AR(1) process. Then we consider Bartlett's formula, which is widely used in time series analysis to provide estimates of the asymptotic covariance between sample autocorrelations, but which is not applicable when the underlying process is nonlinear. Hence, we derive a novel Bartlett-type formula for the asymptotic distribution of the sample autocorrelations of a binomial AR(1) process, which is then applied to develop tests concerning the autocorrelation structure. Simulation studies are carried out to evaluate the size and power of the proposed tests under diverse alternative process models. Several real examples are used to illustrate our methods and findings.     

Correction methods for ties in rank correlations

Equal values are common when rank methods are applied to rounded data or data consisting solely of small integers. A popular technique for resolving ties in rank correlation is the mid-rank method: the mean of the rankings remains unaltered, but the variance is reduced and modified according to the number and location of ties. Although other methods for breaking ties were proposed in the literature as early as 1939, no such procedure has gained such wide acceptance as mid-ranks. This research analyses various techniques for assigning ranks to tied values, with two objectives: (1) to enable the computation of rank correlation coefficients, such as those of Spearman, Kendall and Gini, by using the usual definition applied in the absence of ties, and (2) to determine whether it really makes a difference which of the various techniques is selected and, if so, which technique is most appropriate for a given application.     

Boxplot-Based Outlier Detection for the Location-Scale Family

Boxplots are among the most widely used exploratory data analysis (EDA) tools in statistical practice. Typical applications of boxplots include eliciting information about the underlying distribution (shape, location, etc.) as well as identifying possible outliers. This article focuses on a modification using a type of lower and upper fences similar in concept to those used in a traditional boxplot; however, instead of constructing the upper and lower fences using the upper and lower quartiles, respectively, and a multiple of the interquartile range (IQR), multiples of the upper and the lower semi-interquartile ranges (SIQR), respectively, measured from the sample median, are used. Any observation beyond the proposed fences is labeled a potential outlier. An exact expression for the probability that at least one sample observation is wrongly classified as an outlier, the so-called “some-outside rate per sample” (Hoaglin et al. (1986)), is derived for the family of location-scale distributions and is used in the determination of the fence constants. Tables for the fence constants are provided for a number of well-known location-scale distributions along with some illustrations with data; the performance of the outlier detection rule is explored in a simulation study.     

A Note on Fisher Information and Imperfect Ranked-Set Sampling

We show by example that the Fisher information in an imperfect ranked-set sample may be higher than the Fisher information in a perfect ranked-set sample. This corrects certain misconceptions in the literature. The example also provides an additional counterexample to a common claim about the relationship between imperfect rankings and perfect rankings.     

Variable selection for spatial Poisson point processes via a regularization method

It is often of interest to use regression analysis to study the relationship between occurrence of events in space and spatially-indexed covariates. One model for such regression analysis is the Poisson point process. Here, we develop a method to perform the selection of covariates and the estimation of model parameters simultaneously for this model via a regularization method. We assess the finite-sample properties of our method with a simulation study. In addition, we propose a variant of our method that allows the selection of covariates at multiple pixel resolutions. For illustration, we consider the locations of a tree species, Beilschmiedia pendula, in a study plot at Barro Colorado Island in central Panama. We find that Beilschmiedia pendula occurs in greater abundance at locations with higher elevation and steeper slope. Also, we identify three species to which Beilschmiedia pendula tends to be attracted, two species by which it appears to be repelled, and a species with no apparent relationship.     

A distribution function estimator for the difference of order statistics from two independent samples

For two independent populations X and Y we develop the empirical distribution function estimator for the difference of order statistics of the form X _(i)−Y _(j). The key practical application for this estimator pertains to inference between quantiles from two independent populations.     

A NOTE ON CHARACTERIZATIONS OF DISTRIBUTIONS BY REGRESSIONS OF NON-ADJACENT GENERALIZED ORDER STATISTICS

We investigate the problem of characterizations of distributions by regressions of generalized order statistics (GOSs) based on a continuous distribution function F . We show that F is uniquely determined if the regressions of a GOS given two other consecutive GOSs are known.     

Surgical audit: statistical lessons from Nightingale and Codman

There is a long history of interest in examining and comparing surgical outcomes. The 'epidemiological' approach was initiated by Florence Nightingale in her suggestion for uniform surgical statistics, and she clearly predicted the problems that are associated with collecting, analysing and interpreting such data. Unfortunately those responsible for implementing and reporting her scheme appeared not to have shared her insight. The contrasting 'clinical' approach was championed by Ernest Codman in his search for full and honest appraisals of surgical errors. Once again, despite initial enthusiasm, others had great difficulty in following his example, although we discuss a recent instance of a reflective analysis of an individual surgeon's performance. We conclude by suggesting that a synthesis between these approaches is appropriate, but we follow others in warning of the inevitable extra-statistical difficulties that will arise.