The essentially complete class of rules in multinomial identification

The problem of identification within two groups is considered, when the space 𝔛 of the possible values of the observed random variable X is finite. Using an essentially complete class of tests hypothesis ξ=0 (ξis real) for the multivariate exponential family, an essentially complete class of sample-based identification rules has been found. Comparison of the rules to those derived from density estimators has shown that the latter constitute a subclass of the former.     

Γ-Optimal decision procedures for selecting the best population in randomized complete block design

In randomized complete block design, we face the problem of selecting the best population. If some partial information about the unknown parameters is available, then we wish to delermine the optimal decisin rule to select the best population.

In this paper, in the class of natural selection rules, we employ the Γ-optimal criterion to determine optimal decision rules that will minimize the maximum expected risk over the class of some partial information. Furthermore, the traditional hypothesis testing is briefly discussed from the view point of ranking and selecting.     

A class of modified stein estimators with easily computable risk functions

Consider the problem of estimating the mean of a p (≥3)-variate multi-normal distribution with identity variance-covariance matrix and with unweighted sum of squared error loss. A class of minimax, noncomparable (i.e. no estimate in the class dominates any other estimate in the class) estimates is proposed; the class contains rules dominating the simple James-Stein estimates. The estimates are essentially smoothed versions of the scaled, truncated James-Stein estimates studied by Efron and Morris. Explicit and analytically tractable expressions for their risks are obtained and are used to give guidelines for selecting estimates within the class.     

James-stein estimation with constraints on the norm

Consider the problem of estimating a multivariate mean 0(pxl), p>3, based on a sample x^ ..., xn with quadratic loss function. We find an optimal decision rule within the class of James-Stein type decision rules when the underlying distribution is that of a variance mixture of normals and when the norm ||0|| is known. When the norm is restricted to a known interval, typically no optimal James-Stein type rule exists but we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.     

An essentially complete class of multiple decision procedures

Let π₁,…, π_k represent k(?2) independent populations. The quality of the ith population π_i is characterized by a real-valued parameter θ_i, usually unknown. We define the best population in terms of a measure of separation between θ_i's. A selection of a subset containing the best population is called a correct selection (CS). We restrict attention to rules for which the size of the selected subset is controlled at a given point and the infimum of the probability of correct selection over the parameter space is maximized. The main theorem deals with construction of an essentially complete class of selection rules of the above type. Some classical subset selection rules are shown to belong to this class.     

Accuracy and fairness of rain rules for interrupted one-day cricket matches

In this paper, we investigate the relative merits of rain rules for one-day cricket matches. We suggest that interrupted one-day matches present a missing data problem: the outcome of the complete match cannot be observed, and instead the outcome of the interrupted match, as determined at least in part by the rain rule in question, is observed. Viewing the outcome of the interrupted match as an imputation of the missing outcome of the complete match, standard characteristics to assess the performance of classification tests can be used to assess the performance of a rain rule. In particular, we consider the overall and conditional accuracy and the predictive value of a rain rule. We propose two requirements for a ‘fair’ rain rule, and show that a fair rain rule must satisfy an identity involving its conditional accuracies. Estimating the performance characteristics of various rain rules from a sample of complete one-day matches our results suggest that the Duckworth–Lewis method, currently adopted by the International Cricket Council, is essentially as accurate as and somewhat more fair than its best competitors. A rain rule based on the iso-probability principle also performs well but might benefit from re-calibration using a more representative data base.     

On selecting the best population

This paper deals with the problem of selecting the “best” population from a given number of populations in a decision theoretic framework. The class of selection rules considered is based on a suitable partition of the sample space. A selection rule is given which is shown to have certain optimum properties among the selection rules in the given class for a mal rules are known.     

A new measure of nominal-ordinal association

A new measure for evaluating the strength of the association between a nominal variable and an ordered categorical response variable is introduced. The introduction of a new measure is justified by analysing the characteristics of a measure of the nominal-ordinal association proposed by Agresti (1981), especially with respect to the problem of the 'choice' of a predictive variable. The sample-based version of the index is studied, and its asymptotic standard error and asymptotic distribution are derived. Simulations are considered to evaluate the adequacy of the asymptotic approximation determined, following Goodman & Kruskal (1963).     

Binary designs are not always the best

We give an example of a nonbinary block design which is better than any binary design with respect to the E-optimality criterion. This shows that the class of binary designs is not essentially complete, at least with respect to E-optimality.     

Characterizations of arcsin and related distributions based on a new generalized unimodality

A general characterization for α-unimodal distributions was provided in [Alamatsaz, M.H. 1985: A Note on an Article by Artikis, Acta Mathematica Hungarica 45, 159–162] and its extension to a multivariate case in [Alamatsaz, M.H. 1993: On Characterizations of Exponential and Gamma Distributions, Statistics and Probability Letters 17, 315–319]. Here, by solving the related equations, another generalization for unimodality is presented. As a result of this generalization, a simpler proof of a conjecture, as well as a characterization for generalized arcsin distributions and some generalizations of the author’s earlier works, is obtained. Last, but not the least, it is shown that some elementary methods can be more powerful than some more advanced techniques.     

Linear rank tests for censored survival data

We describe a class of rank test procedures for the two-sample problem with right censored survival data. The class of tests is directly generalized from the linear rank tests by assigning each observation a rank according to its corresponding Wilcoxon scores. It allows a flexible choice of score functions, in particular, those powerful against scale differences between the two survival distributions. Monte Carlo simulations have shown that some members of this class have great power in detecting crossing-curve alternatives (alternatives where underlying survival curves cross over). The class also contains tests essentially equivalent to the Gehan-Wilcoxon and the logrank tests.     

A general class of poverty measures

Measurement of poverty in the spirit of Sen essentially consists of two steps, namely (1) the identification of the poor and (2) the aggregation of the income distribution of the poor into an indicator called poverty measure. We contribute to the second step from a mathematical and statistical point of view by defining a class of poverty measures and investigating its properties including sensitivity with respect to changes in the income distribution. Various poverty orderings are defined and their relation to stochastic dominance is investigated. Finally estimation of the class of poverty measures from individual and grouped data is considered.     

A class of treatment assignment rules for sequential experiments

In an experiment to compare K(<2) treatments, suppose that eligible subjects arrive at an experimental site sequentially and must be treated immediately. In this paper, we assume that the size of the experiment cannot be predetermined and propose and analyze a class of treatment assignment rules which offer compromises between the complete randomization and the perfect balance schemes, A special case of these assignment rules is thoroughly investigated and is featured in the numerical compu-tations. For practical use, a method of implementation of this special rule is provided.     

Verallgemeinerte bayes-verfahren bei sequentiellen testproblemen

In this paper, problems of sequential decision theory are taken into consideration by extending the definition of the BAYES rule and treating BAYES rules. This generalisation is quite useful for practice. In many cases only BAYES rules can be calculated. The conditions under which such sequential decision procedures exist are demonstrated, as well as how to construct them on a scheme of backward induction resulting in the conclusion that the existence of BAYES rules needs essentially weaker assumptions than the existence of BAYES rules.Futhermore, methods are searched to simplify the construction of optimal stopping rules. Some illustrative examples are given.     

Inference rules and inferential distributions

We introduce the concept of inferential distributions corresponding to inference rules. Fiducial and posterior distributions are special cases. Inferential distributions are essentially unique. They correspond to or represent inference rules and are defined on the parameter space. Not all inference rules can be represented by an inferential distribution. A constructive method is given to investigate its existence for any given inference rule.     

Simultaneous selection and estimation in general linear models

The problem of selecting the largest treatment parameter, and simultaneously estimating the selected treatment parameter, in a general linear model is considered in the decision theoretic Bayes approach. Both cases, where the error variance is known or unknown, are included. Bayes decision rules are derived for noninformative priors and for normal priors. The problem of finding Bayes designs, i.e. designs that have minimum Bayes risk, within a given class of designs is also discussed.     

Edge Estimation in the Population of a Binary Tree Using Node-Sampling

Suppose a finite population of several vertices, each connected to single or multiple edges. This constitutes a structure of graphical population of vertices and edges. As a special case, the graphical population like a binary tree having only two child vertices associated to parent vertex is taken into consideration. The entire binary tree is divided into two sub-graphs such as a group of left-nodes and a group of right-nodes. This paper takes into account a mixture of graph structured and population sampling theory together and presents a methodology for mean-edge-length estimation of left sub-graph using right edge sub-graph as an auxiliary source of information. A node-sampling procedure is developed for this purpose and a class of estimators is proposed containing several good estimators. Mathematical conditions for minimum bias and optimum mean squared error of the class are derived and theoretical results are numerically supported with a test of 99% confidence intervals. It is shown that suggested class has a sub-class of optimum estimators, and sample-based estimates are closer to the true value of the population parameter.     

Moments of sample moments

The problem offinding expressions for sampling moments of sample moments has been ahistorically old one. This problem is treated here, with the use of partitions and multi partitions , for the univariate as well as the multivariate case. The systematic combinatorial approach minimizes the chance of omitting any

contributions and making errors in their computation. Componentwise identification is made possible , soerrors can be located. From the complete set of general moment formulae, s pecial cases may be obtained by identifying identical variables.     

Sequential classification on partially ordered sets

Summary. A general theorem on the asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to 1 almost surely and determining optimal rates of convergence. Properties of a class of experiment selection rules are explored.     

Comment on ‘An improved score interval with a modified midpoint for a binomial proportion’

Yu et al. [An improved score interval with a modified midpoint for a binomial proportion. J Stat Comput Simul. 2014;84:1022–1038] propose a novel confidence interval (CI) for a binomial proportion by modifying the midpoint of the score interval. This CI is competitive with the various commonly used methods. At the same time, Martín and Álvarez [Two-tailed asymptotic inferences for a proportion. J Appl Stat. 2014;41:1516–1529] analyse the performance of 29 asymptotic two-tailed CI for a proportion. The CI they selected is based on the arcsin transformation (when this is applied to the data increased by 0.5), although they also refer to the good behaviour of the classical methods of score and Agresti and Coull (which may be preferred in certain circumstances). The aim of this commentary is to compare the four methods referred to previously. The conclusion (for the classic error α of 5%) is that with a small sample size (≤80) the method that should be used is that of Yu et al.; for a large sample size (n?≥?100), the four methods perform in a similar way, with a slight advantage for the Agresti and Coull method. In any case the Agresti and Coull method does not perform badly and tends to be conservative. The program which determines these four intervals are available from the address http://www.ugr.es/local/bioest/Z_LINEAR_K.EXEhttp://www.ugr.es/local/bioest/Z_LINEAR_K.EXE.