Econometric Analysis of Costing System Components in Rail Rate Regulation

In response to Congressional directive, the Interstate Commerce Commission (ICC) has created a railroad costing system that includes as key components ratios designed to estimate variable costs associated with freight transportation. The estimated variability ratios are used to determine freight surcharges, jurisdictional threshold rates, and basic rail rates in administrative law and federal court proceedings. In this article we assess the quality and reliability of the estimated variability ratios and their components against standards from economic theory and statistical theory and practice. Our work includes reproduction of the naive ICC regressions, updated naive regressions for the latest data set, estimation based on more secure econometric foundations, and sensitivity analyses comparing alternative estimation procedures. Fundamental questions arise concerning the scientific and evidentiary standards that are required for econometric methodology in policy making and regulatory activities.     

Calibrating predictive distributions

This paper concerns prediction from the frequentist point of view. The aim is to define a well-calibrated predictive distribution giving prediction intervals, and in particular prediction limits, with coverage probability equal or close to the target nominal value. This predictive distribution can be considered in a number of situations, including discrete data and non-regular cases, and it is founded on the idea of calibrating prediction limits to control the associated coverage probability. Whenever the computation of the proposed distribution is not feasible, this can be approximated using a suitable bootstrap simulation procedure or by considering high-order asymptotic expansions, giving predictive distributions already known in the literature. Examples and applications of the results to different contexts show the wide applicability and the very good performance of the proposed predictive distribution.     

Rate of convergence for the distribution of the spearman-karber estimator

A Berry-Esseen type of bound is obtained for the error of the normal approximation to the distribution of the Spearman-Karber estimator. It is shown that this bound is of the order of the square root of the common dose mesh.     

Stochastic approximation methods in linear regression models (with consideration of errors in the regressors) 1

Usually, the dependence in stationary processes is described by a set of coefficients. In this paper, a measure of dependence is proposed which can be used instead of the autocorrelation function, and another measure for the dependence between two processes instead of cross-correlation function and coherence coefficients. In the end, an improvement of extrapolation of a process is investigated which is caused by the knowledge of another related process.     

Bootstrap approaches for estimation and confidence intervals of long memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296–1301] and on the Durbin–Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.     

Nonparametric estimators for shift in quantal bioassay

Let F(x) and F(x+θ) be log dose-response curves for a standard preparation and a test preparation, respectively, in a parallel quantal bioassay designed to test the relative potency of a drug, toxicant, or some other substance, and suppose the form of F is unknown. Several estimators of the shift parameter θ or relative potency, are compared, including some generalized and trimmed Spearman-Kärber estimators and a non parametric maximum likelihood estimator. Both point and interval estimation are discussed. Some recommendations concerning the choices of estimators are offered.     

Efficient estimators for adaptive stratified sequential sampling

In stratified sampling, methods for the allocation of effort among strata usually rely on some measure of within-stratum variance. If we do not have enough information about these variances, adaptive allocation can be used. In adaptive allocation designs, surveys are conducted in two phases. Information from the first phase is used to allocate the remaining units among the strata in the second phase. Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation sampling design – where the final sample size was random – and an unbiased estimator. Here, we derive an unbiased variance estimator for the design, and consider a related design where the final sample size is fixed. Having a fixed final sample size can make survey-planning easier. We introduce a biased Horvitz–Thompson type estimator and a biased sample mean type estimator for the sampling designs. We conduct two simulation studies on honey producers in Kurdistan and synthetic zirconium distribution in a region on the moon. Results show that the introduced estimators are more efficient than the available estimators for both variable and fixed sample size designs, and the conventional unbiased estimator of stratified simple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator with the introduced estimators. Simulation results show that the introduced estimators are more efficient than available estimators of these well-known adaptive allocation designs.     

Recurrence relations for single and product moments of order statistics from a generalized half logistic distribution with applications to inference

In this paper, we derive several recurrence relations satisfied by the single and product moments of order statistics from a generalized half logistic distribution. These generalize the corresponding results for the half logistic distribution established by Balakrishnan (1985). The relations established in this paper will enable one to compute the single and product moments of all order statistics for all sample sizes in a simple recursive manner; this may be done for any choice of the shape parameter k. These moments can then be used to determine the best linear unbiased estimators of location and scale parameters from complete as well as Type-I1 censored samples.     

Design-based confidence limits for a distribution function

A method for constructing confidence limits for a distribution function is proposed. This method is a simple modification of the common method based on a normal approximation to the distribution of the estimated distribution function. The methods differ in how the estimated standard errors are used. The coverage properties of the two methods are compared in a simulation study. Coverage probabilities for the proposed method are found to be much closer to the nominal levels, particularly in the tails of the population distribution.     

A ridge-type estimator and good prior means

Swindel (1976) introduced a modified ridge regression estimator based on prior information. A necessary and sufficient condition is derived for Swindel's proposed estimator to have lower risk than the conventional ordinary ridge regression estimator when both estimators are computed using the same value of k.