Three‐Stage Decision‐Making Model under Restricted Conditions for Emergency Response to Ships Not under Control

A ship that is not under control (NUC) is a typical incident that poses serious problems when in confined waters close to shore. The emergency response to NUC ships is to select the best risk control options, which is a challenge in restricted conditions (e.g., time limitation, resource constraint, and information asymmetry), particularly in inland waterway transportation. To enable a quick and effective response, this article develops a three‐stage decision‐making framework for NUC ship handling. The core of this method is (1) to propose feasible options for each involved entity (e.g., maritime safety administration, NUC ship, and ships passing by) under resource constraint in the first stage, (2) to select the most feasible options by comparing the similarity of the new case and existing cases in the second stage, and (3) to make decisions considering the cooperation between the involved organizations by using a developed Bayesian network in the third stage. Consequently, this work provides a useful tool to achieve well‐organized management of NUC ships.     

A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao-Cramer lower bound) in the limit of small noise.     

Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

Outlier detection algorithms are intimately connected with robust statistics that down‐weight some observations to zero. We define a number of outlier detection algorithms related to the Huber‐skip and least trimmed squares estimators, including the one‐step Huber‐skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.     

Population structure and correlation between auxiliary and target variables may affect precision of estimates in forest inventory

Simulations of forest inventory in several populations compared simple random with “quick probability proportional to size” (QPPS) sampling. The latter may be applied in the absence of a list sampling frame and/or prior measurement of the auxiliary variable. The correlation between the auxiliary and target variables required to render QPPS sampling more efficient than simple random sampling varied over the range 0.3–0.6 and was lower when sampling from populations that were skewed to the right. Two possible analytical estimators of the standard error of the estimate of the mean for QPPS sampling were found to be less reliable than bootstrapping.     

Trend smoothness achieved by penalized least squares with the smoothing parameter chosen by optimality criteria

This work presents a study about the smoothness attained by the methods more frequently used to choose the smoothing parameter in the context of splines: Cross Validation, Generalized Cross Validation, and corrected Akaike and Bayesian Information Criteria, implemented with Penalized Least Squares. It is concluded that the amount of smoothness strongly depends on the length of the series and on the type of underlying trend, while the presence of seasonality even though statistically significant is less relevant. The intrinsic variability of the series is not statistically significant and its effect is taken into account only through the smoothing parameter.     

Marginal likelihood estimation from the Metropolis output: tips and tricks for efficient implementation in generalized linear latent variable models

The marginal likelihood can be notoriously difficult to compute, and particularly so in high-dimensional problems. Chib and Jeliazkov employed the local reversibility of the Metropolis–Hastings algorithm to construct an estimator in models where full conditional densities are not available analytically. The estimator is free of distributional assumptions and is directly linked to the simulation algorithm. However, it generally requires a sequence of reduced Markov chain Monte Carlo runs which makes the method computationally demanding especially in cases when the parameter space is large. In this article, we study the implementation of this estimator on latent variable models which embed independence of the responses to the observables given the latent variables (conditional or local independence). This property is employed in the construction of a multi-block Metropolis-within-Gibbs algorithm that allows to compute the estimator in a single run, regardless of the dimensionality of the parameter space. The counterpart one-block algorithm is also considered here, by pointing out the difference between the two approaches. The paper closes with the illustration of the estimator in simulated and real-life data sets.     

Bayes shrinkage estimator for consistency assessment of treatment effects in multi-regional clinical trials

The primary objective of a multi-regional clinical trial is to investigate the overall efficacy of the drug across regions and evaluate the possibility of applying the overall trial result to some specific region. A challenge arises when there is not enough regional sample size. We focus on the problem of evaluating applicability of a drug to a specific region of interest under the criterion of preserving a certain proportion of the overall treatment effect in the region. We propose a variant of James-Stein shrinkage estimator in the empirical Bayes context for the region-specific treatment effect. The estimator has the features of accommodating the between-region variation and finiteness correction of bias. We also propose a truncated version of the proposed shrinkage estimator to further protect risk in the presence of extreme value of regional treatment effect. Based on the proposed estimator, we provide the consistency assessment criterion and sample size calculation for the region of interest. Simulations are conducted to demonstrate the performance of the proposed estimators in comparison with some existing methods. A hypothetical example is presented to illustrate the application of the proposed method.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

LS estimation of periodic autoregressive models with non-Gaussian errors: a simulation study

In this article, the least squares (LS) estimates of the parameters of periodic autoregressive (PAR) models are investigated for various distributions of error terms via Monte-Carlo simulation. Beside the Gaussian distribution, this study covers the exponential, gamma, student-t, and Cauchy distributions. The estimates are compared for various distributions via bias and MSE criterion. The effect of other factors are also examined as the non-constancy of model orders, the non-constancy of the variances of seasonal white noise, the period length, and the length of the time series. The simulation results indicate that this method is in general robust for the estimation of AR parameters with respect to the distribution of error terms and other factors. However, the estimates of those parameters were, in some cases, noticeably poor for Cauchy distribution. It is also noticed that the variances of estimates of white noise variances are highly affected by the degree of skewness of the distribution of error terms.     

Smooth tail-index estimation

The two parametric distribution functions appearing in the extreme-value theory – the generalized extreme-value distribution and the generalized Pareto distribution – have log-concave densities if the extreme-value index γ∈[?1, 0]. Replacing the order statistics in tail-index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density ? f _n leads to novel smooth quantile and tail-index estimators. These new estimators aim at estimating the tail index especially in small samples. Acting as a smoother of the empirical distribution function, the log-concave distribution function estimator reduces estimation variability to a much greater extent than it introduces bias. As a consequence, Monte Carlo simulations demonstrate that the smoothed version of the estimators are well superior to their non-smoothed counterparts, in terms of mean-squared error.