On the foundations of decision making under partial information

We show how to model incompleteness in the decision maker's judgements, within a Bayesian context, providing axioms which lead us to work with families of values or probabilities and utilities. The proper solution concepts are suggested. On the whole, we provide a more robust decision theory, based on a weaker set of axioms, but embodying coherence, since it essentially implies carrying out a family of coherent decision analyses.     

Treatment with human chorionic gonadotropin for PADAM: A preliminary report

The purpose of this study was to evaluate the efficacy and safety of human chorionic gonadotropin (hCG) for patients with partial androgen deficiency of the aging male (PADAM). Twenty-one patients over 50 years of age with PADAM symptoms were included in this study. Laboratory and endocrinologic profiles were reviewed as appropriate, and PADAM symptoms were judged by means of several questionnaires such as the Aging Males' Symptoms (AMS) scale, short version of the International Index of Erectile Function (IIEF-5), and the Self-rating Depression Scale (SDS). Laboratory and endocrinologic values and symptom scores were evaluated and compared before and after treatment by hCG injection. The treatment period was 8.0 ± 5.0 months (3.0 – 24.0 months). Serum concentrations of testosterone, including total testosterone, calculated free testosterone, and calculated bioavailable testosterone, increased significantly. AMS total scores and subscores decreased significantly after treatment. However, IIEF-5 and SDS scores did not improve. With respect to adverse effects, laboratory tests showed that only red blood cell count, hematocrit and hemoglobin level increased significantly after treatment, however, these values remained within the normal range. No adverse effect was identified after treatment. We conclude that hCG injection may be considered as a treatment for PADAM.     

Optimal paired comparison designs for first-order interactions

In many fields of applications paired comparisons are used in which either full or partial profiles of the alternatives are presented. For this situation we introduce an appropriate model and derive optimal designs in the presence of interactions when all attributes have the same number of levels.     

Set Identified Linear Models

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z^⊤(xβ−y)) = E(z^⊤u(z)), where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a setup. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest, but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When B is a strictly convex set, we also construct a test of the null hypothesis, β₀∈B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B− {β₀}. Results of some Monte Carlo experiments are presented.     

A Class of Multidimensional Latent Class IRT Models for Ordinal Polytomous Item Responses

We propose a class of multidimensional Item Response Theory models for polytomously-scored items with ordinal response categories. This class extends an existing class of multidimensional models for dichotomously-scored items in which the latent abilities are represented by a random vector assumed to have a discrete distribution, with support points corresponding to different latent classes in the population. In the proposed approach, we allow for different parameterizations for the conditional distribution of the response variables given the latent traits, which depend on the type of link function and the constraints imposed on the item parameters. Moreover, we suggest a strategy for model selection that is based on a series of steps consisting of selecting specific features, such as the dimension of the model (number of latent traits), the number of latent classes, and the specific parameterization. In order to illustrate the proposed approach, we analyze a dataset from a study on anxiety and depression on a sample of oncological patients.     

Optimal Designs for Best Linear Unbiased Prediction in Diallel Crosses

ABSTRACT

Recently, Ghosh and Das (2003 Ghosh , H. , Das , A. ( 2003 ). Optimal diallel cross designs for estimation of heritability . J. Statist. Plann. Inference 116 : 185 – 196 . [Google Scholar]) considered the estimation of variance components and the variances of these estimates. While comparing the yielding capacities of the cross (i, j), Kempthorne and Curnow (1961 Kempthorne , O. , Curnow , R. N. ( 1961 ). The partial diallel cross . Biometrics 17 : 229 – 250 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed the estimation of the yielding capacity of any cross based on the least square estimators of the general combining ability effects and/or the mean yield of the cross (i, j). In this article, the problem of predicting the yielding capacity of the cross (i, j) from the sample of inbred lines has been considered. The properties of the best linear unbiased predictor for predicting the unobserved general combining ability effects together with general mean effect has been studied. We characterize A-optimal complete diallel cross designs and some efficient partial diallel cross designs under this setup.     

Optimal Routing Among ⋅/M/1 Queues with Partial Information

Abstract

When routing dynamically randomly arriving messages, the controller of a high-speed communication network very often gets the information on the congestion state of down stream nodes only after a considerable delay, making that information irrelevant at decision epochs. We consider the situation where jobs arrive according to a Poisson process and must be routed to one of two (parallel) queues with exponential service time distributions (possibly with different means), without knowing the congestion state in one of the queues. However, the (conditional) probability distribution of the state of the unobservable queue can be computed by the router. We derive the joint probability distribution of the congestion states in both queues as a function of the routing policy. This allows us to identify optimal routing schemes for two types of frameworks: global optimization, in which the weighted sum of average queue lengths is minimized, and individual optimization, in which the goal is to minimize the expected delay of individual jobs.     

Partial self-exciting point processes and their parameter estimations

Abstract

A partial self-exciting point process is proposed based on some phenomena in real world, which is a new kind of Hawkes process with partial self-exciting effect. The features, properties and moments of the partial self-exciting point process are investigated in terms of Dynkin formula and the method proposed by Cui et al. (2017 Cui, L., Hawkes, R. A. G. Yi. and H. 2017. A new method for moments of Hawkes processes. (submitted). [Google Scholar]), and the relationship between the new and conventional Hawkes processes is given. The maximum-likelihood estimations (MLEs) for the parameters in the partial self-exciting point process for two data situations are given via some sets of equations that can be solved numerically by suing the commend fslove in Matlab. Some numerical examples are presented based on simulation data to illustrate the MLE method, and an algorithm to generate the random event times for the partial self-exciting point process is presented as well. A primary goal of the work is to extend the applicability of Hawkes process and to present the MLE of parameters for partial self-exciting point process.     

Block–Savits Characterization and Star Ordering of Exponential Mixtures

Block and Savits (1980 Block , H. W. , Savits , T. H. ( 1980 ). Laplace transforms for classes of life distributions . Ann. Probab. 8 : 465 – 474 .[Crossref], [Web of Science ®] , [Google Scholar]) established a characterization of life distributions using the Laplace transform. In this article, we remark that one of the necessary conditions to be IFRA distribution is equivalent to the star ordering of exponential mixtures. It leads to the definition of two new classes of life distributions, called LIFR and LIFRA, and their dual classes: LDFR and LDFRA. It occurs that these classes have many useful aging properties and preserve known reliability operations. Properties of the classes are studied and relations with known classes are established.     

A Stepwise AIC Method for Variable Selection in Linear Regression

In this article, we study stepwise AIC method for variable selection comparing with other stepwise method for variable selection, such as, Partial F, Partial Correlation, and Semi-Partial Correlation in linear regression modeling. Then we show mathematically that the stepwise AIC method and other stepwise methods lead to the same method as Partial F. Hence, there are more reasons to use the stepwise AIC method than the other stepwise methods for variable selection, since the stepwise AIC method is a model selection method that can be easily managed and can be widely extended to more generalized models and applied to non normally distributed data. We also treat problems that always appear in applications, that are validation of selected variables and problem of collinearity.