An application of negative binomial distribution of order k in sensitive surveys

This article is an attempt to generalize some of the recent papers on randomized response techniques by using the negative binomial distribution of order k to randomize the responses in the randomization design where respondents can report outcome of one of two binary devices depending upon their actual status. The relative efficiency results are observed to be better than those of many recent and relevant randomized response techniques. The results are also better than those of the base line model used in this study, providing the sensitive attribute is rare. An extra advantage of the proposed technique is that it does not require any additional sampling and administrative cost.     

THE OPTIMAL TEST FOR SELECTING THE GREATER OF TWO BINOMIAL PROBABILITIES

The efficiency of a sequential test is related to the “importance” of the trials within the test. This relationship is used to find the optimal test for selecting the greater of two binomial probabilities, p_α and p_b, namely, the stopping rule is “gambler's ruin” and the optimal discipline when p_α+p_b≤ 1 (≥ 1) is play-the-winner (loser), i.e. an α-trial which results in a success is followed by an α-trial (b-trial) whereas an α-trial which results in a failure is followed by α b-trid (α-trial) and correspondingly for b-trials.     

具扩散项的停止-损失再保问题的破产概率

本文在具有扩散项的假定下,研究了原保险公司、再保险公司的破产问题.在索赔随机变量为指数情形,得到了免赔额与破产概率之间的关系,并且得到了如下的结果:1.随机风险模型生存概率的表达公式,从而得到了由扰动导致的破产概率的表达公式.2.分别得到了两类保险公司破产概率的表达公式.所得结果不仅推广了文献[1]的结果,而且使用的方法具有一定的独立价值.     

Analysing state dependences in emotional experiences by dynamic count data models

Summary. The paper presents a multilevel framework for the analysis of multivariate count data that are observed over several time periods for a random sample of individuals. The approach proposed facilitates studying observed and unobserved sources of dependences among the event categories in the presence of possibly higher order autoregressive effects. In an investigation of the relationships between pleasant and unpleasant emotional experiences and the personality traits neuroticism and extraversion over time, we find that the two personality factors are related to both the mean rates of the emotional experiences and their carry-over effects. Respondents with high neuroticism scores not only reported more unpleasant than pleasant emotional experiences but also exhibited higher carry-over effects for unpleasant than for pleasant emotions. In contrast, respondents with high extraversion scores reported fewer anxiety and more euphoria emotions than respondents with low extraversion scores with weaker carry-over effects for both pleasant and unpleasant emotions.     

Uncertainty with Partial Information on the Possibility of the Events

The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for instance, the information that there are more white balls than black ones). Some implications are shown with regard to the core of the capacity and to two additive measures which can be derived from capacities: the Shapley value and the nucleolus. Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative information inequalities, and the Shapley value does it more strictly than the nucleolus. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measure of Asymmetry for Square Contingency Tables Having Ordered Categories

For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent the degree of departure from symmetry. This paper proposes a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed using the Cressie–Read power-divergence or Patil–Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j (> i ) or above. The measure depends on the order of listing the categories. It should be useful for comparing the degree of asymmetry in several tables with ordered categories. The relationship between the measure and the normal distribution is shown.     

Mean-Minimum Exact Confidence Intervals

This article introduces mean-minimum (MM) exact confidence intervals for a binomial probability. These intervals guarantee that both the mean and the minimum frequentist coverage never drop below specified values. For example, an MM 95[93]% interval has mean coverage at least 95% and minimum coverage at least 93%. In the conventional sense, such an interval can be viewed as an exact 93% interval that has mean coverage at least 95% or it can be viewed as an approximate 95% interval that has minimum coverage at least 93%. Graphical and numerical summaries of coverage and expected length suggest that the Blaker-based MM exact interval is an attractive alternative to, even an improvement over, commonly recommended approximate and exact intervals, including the Agresti–Coull approximate interval, the Clopper–Pearson (CP) exact interval, and the more recently recommended CP-, Blaker-, and Sterne-based mean-coverage-adjusted approximate intervals.     

Bayesian Dividend Optimization and Finite Time Ruin Probabilities

We consider the valuation problem of an (insurance) company under partial information. Therefore, we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We state a numerical procedure for approximating both the optimal dividend strategy and the corresponding value function. Furthermore, threshold strategies are discussed in some detail. Finally, we calculate the probability of ruin in the uncontrolled and controlled situation.     

Likelihood inference for correlated binary data without any information about the joint distributions

We propose a universal robust likelihood that is able to accommodate correlated binary data without any information about the underlying joint distributions. This likelihood function is asymptotically valid for the regression parameter for any underlying correlation configurations, including varying under- or over-dispersion situations, which undermines one of the regularity conditions ensuring the validity of crucial large sample theories. This robust likelihood procedure can be easily implemented by using any statistical software that provides naïve and sandwich covariance matrices for regression parameter estimates. Simulations and real data analyses are used to demonstrate the efficacy of this parametric robust method.     

Improper priors for translation families

We consider the problem of inference when sampling from a translation family with an improper prior. Properties of the formal Bayes inference will be studied. We give conditions (on the prior and/or the family) guaranteeing the HS-coherence (see Heath and Sudderth, Ann. Statist. 6 (1978), 333–345) of the formal Bayes posterior. Since HS-coherence is equivalent to being a posterior of a finitely additive prior, all coherence results imply the existence of a finitely additive prior which has the formal Bayes inference as a posterior.