Characterizations of bivariate distributions using concomitants of record values

In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We have also derived properties of concomitants of record values which characterize each of the following families viz Morgenstern family, bivariate Pareto family and a generalized Gumbel’s family of bivariate distributions. Some applications of the characterization results are discussed and important conclusions based on the characterization results are drawn.     

On characterizations of distributions by expected values of order statistics and record values with gap

In this paper, we obtain some recurrence relationships for conditional expectations of nonadjacent order statistics and record values when the distribution function is absolutely continuous, and we prove that the distribution function is uniquely determined by the distribution of conditioned record values and by the expected values of these records. Further, different distributions are characterized by these relationships.     

Recurrence relations for moment and conditional moment generating functions of generalized order statistics

In this paper, we obtain recurrence relations for moment and conditional moment generating functions of generalized order statistics (gos) based on random samples drawn from a population whose distribution is a member of a doubly truncated class of distributions denoted by . Members of the class are characterized in Section (2) based on recurrence relations for moment generating functions (moments) of gos. In Section (3), we shall characterize members of the class based on recurrence relations for conditional moment generating functions (conditional moments) of gos. These results are specialized to the left, right and non-truncated cases. Ordinary order statistics and ordinary record values are also obtained as special cases of the gos. Characterizations of some members of class such as the Weibull, compound Weibull, Pareto, power function (beta is a special case), Gompertz and compound Gompertz distributions are given as illustrative examples.     

Distributional Properties of Record Values from the Geometric Distribution

Some distributional properties of the record values of non–identically distributed random variables having geometric distributions are discussed. Three theorems dealing with the characterization of the geometric distribution based on these distributional properties are presented. The unique minimum variance unbiased estimators of some functions of the parameters of the distribution and various predictors of the s–th record valued utilizing the first m(m相似文献   

Precedence-type tests based on record values

Precedence-type tests based on order statistics are simple and efficient nonparametric tests that are very useful in the context of life-testing, and they have been studied quite extensively in the literature; see Balakrishnan and Ng (Precedence-type tests and applications. Wiley, Hoboken, 2006). In this paper, we consider precedence-type tests based on record values and develop specifically record precedence test, record maximal precedence test and record-rank-sum test. We derive their exact null distributions and tabulate some critical values. Then, under the general Lehmann alternative, we derive the exact power functions of these tests and discuss their power under the location-shift alternative. We also establish that the record precedence test is the uniformly most powerful test for testing against the one-parameter family of Lehmann alternatives. Finally, we discuss the situation when we have insufficient number of records to apply the record precedence test and then make some concluding remarks.     

Fisher information in record data

We present some general results on Fisher information (FI) contained in upper (or lower) record values and associated record times generated from a sequence of i.i.d. continuous variables. For the record data obtained from a random sample of fixed size, we establish an interesting relationship between its FI content and the FI in the data consisting of sequential maxima. We also consider the record data from an inverse sampling plan (Samaniego and Whitaker, 1986). We apply the general results to evaluate the FI in upper as well as lower records data from the exponential distribution for both sampling plans. Further, we discuss the implication of our results to statistical inference from these record data. Received: December 2001 Acknowledgements. This research was supported by Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) grants 7990089 and 1010222 of Chile. We would like to thank the Department of Statistics at the University of Concepción for its hospitality during the stay of H. N. Nagaraja in Chile in March of 2000, when the initial work was done. We are grateful to the two referees for various comments that let to improvements in the paper.     

Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543–547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.     

Bayesian estimation based on ranked set sample from Morgenstern type bivariate exponential distribution when ranking is imperfect

In this paper we consider Bayes estimation based on ranked set sample when ranking is imperfect, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. Bayes estimators under squared error loss function and LINEX loss function for the mean of the study variate Y, when (X, Y) follows a Morgenstern type bivariate exponential distribution, are obtained based on both usual ranked set sample and extreme ranked set sample. Estimation procedures developed in this paper are illustrated using simulation studies and a real data.     

A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations

In this paper we consider a class of partially adaptive one-step M-estimators for the non-linear regression model with dependent observations. Those estimators adapt themselves with respect to a measure of the tailthickness of the disturbance distribution (as well as to a measure of the scale). The large-sample behavior of those estimators is examined theoretically for general disturbance distributions and numerically for various specific ones. The estimators considered are motivated by the Student-t maximum-likelihood estimator. Given appropriate specifications of the adaptation parameter the estimators are asymptotically efficient on the family of Student-t distributions including the normal distribution.     

Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility

In this paper, we propose two estimators, an integral estimator and a discretized estimator, for the wavelet coefficient of regression functions in nonparametric regression models with heteroscedastic variance. These estimators can be used to test the jumps of the regression function. The model allows for lagged-dependent variables and other mixing regressors. The asymptotic distributions of the statistics are established, and the asymptotic critical values are analytically obtained from the asymptotic distribution. We also use the test to determine consistent estimators for the locations of change points. The jump sizes and locations of change points can be consistently estimated using wavelet coefficients, and the convergency rates of these estimators are derived. We perform some Monte Carlo simulations to check the powers and sizes of the test statistics. Finally, we give practical examples in finance and economics to detect changes in stock returns and short-term interest rates using the empirical wavelet method.     

A general procedure of estimating the population variance when coefficient of variation of an auxiliary variable is known in sample surveys

This paper deals with the problem of estimating population variance ${{S}_{\rm y}^2}$ of the study variable y. We have suggested a family of estimators of population variance ${{S}_{\rm y}^2}$ using the transformations on both the study variable and the auxiliary variable when coefficient of variation of an auxiliary variable x is known. The suggested family of estimators is very wide from which we can generate many estimators by putting the suitable values of scalars. The bias and mean squared error have been obtained upto the first order of approximation. The empirical study is carried out to the support of the suggested family of estimators.     

On the estimation of location parameters in the multivariate one sample and two sample problems

Summary In this paper we consider the problem of estimating the vectors of location parameters in the multivariate one sample and two sample problems. These estimators are obtained through the use of the multivariate rank order statistics such as theWilcoxon or the normal scores statistic considered by the authors inPuri, Sen [1966] andSen, Puri [1967] for the corresponding testing problems. The distribution of these estimators is shown to be symmetric with respect to the parameters being estimated. These estimators are translation invariant, robust and asymptotically normal. Their asymptotic relative efficiencies with respect to the estimators based on the vector of means and medians are discussed by applying the criterion ofWilks generalized variance [Anderson, p. 166]. In particular, it is shown that the estimators based on the multivariate normal scores statistics are asymptotically as efficient as the ones based on the method of least squares when the parent distributions are normal. Research sponsored by National Science Foundation Grant No. GP-12462, and by Research Grant, GM-12868 from the N.I.H., Public Health Service.     

Probability distributions of two-component soil samples

Mixing of sand layers on top of peat soils is achieved by soil improvement machines. The result of the mixing process is studied by taking samples from a vertical cross-section of the profile. The samples will have various values of the sand to peat volume-ratio. These values can be plotted in emperical cumulative frequency distributions. The distributions for two types of machines were found to be quite different due to differences of mixing intensities. A method is proposed for the evaluation of the mixing effect expressed in the parameters of theoretical probability distributions of two-component soil samples. The probability distribution of the volume-ratios in the sample are derived and their properties are discussed. Moment estimators of the parameters are derived. The theoretical distributions are compared with two experimental results obtained with a mixing rooter and a rotary mixer respectively.     

Direct and iterated multistep AR methods for difference stationary processes

The paper focuses on a comparison between the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors. The methods are based on an encompassing representation for the two predictors, which enables us to derive their properties quite easily under a maintained model. The paper provides an analytical expression for the mean square forecast error of the two predictors and derives useful recursive formulae for computing the direct and iterated coefficients. From an empirical standpoint, we propose estimators of the AR coefficients based on the tapered Yule-Walker estimates; we also provide a test of equal forecast accuracy which is very simple to implement and whose critical values are obtained using the bootstrap method.     

Binary effectivity rules

A social choice rule (SCR) is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some SCR. A SCR is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary SCR. A binary SCR is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary SCR. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann–Morgenstern solutions play an important role in this characterization.     

Ratio cum product method of estimation

Summary In this paper methods of estimation which may be considered as combination of ratio and product methods have been suggested. The mean square errors of these estimators utilizing two supplementary variables are compared with (i) simple unbiased estimator (p=0), (ii) usual ratio and product methods of estimation (p=1) and (iii) multivariate ratio and multivariate product estimators (p=2), wherep is the number of supplementary variables utilized. Conditions for their efficient use have been obtained for each case. Extension to general case ofp-variables has been briefly discussed. A new criteria for the efficient use of product estimator have been obtained.     

On the Fisher information in record values

In this article, we establish some general results concerning the comparison of the amount of the Fisher information contained in n record values with the Fisher information contained in n iid observations from the original distribution. Some common distributions are classified according to this criterion. We also propose some methods of estimation based on record values. The results may be of interest in some life testing problems. Received: September 1999     

On the nearness of record values to order statistics from Pitman’s measure of closeness

In the two-sample prediction problem, record values from the present sample may be used as predictors of order statistics from a future sample. In this paper, we investigate the nearness of record statistics (upper and lower) to order statistics from a location-scale family of distributions in the sense of Pitman closeness and discuss the corresponding monotonicity properties. We then determine the closest record value to a specific order statistic from a future sample. Even though in general it depends on the parent distribution, exact and explicit expressions are derived for the required probabilities in the case of exponential and uniform distributions, and some computational results are presented as well. Finally, we consider the mean squared error criterion and examine the corresponding results in the exponential case.     

Farsighted house allocation

In this note we study von Neumann–Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2010) shows that the set of competitive allocations coincides with the unique von Neumann–Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann–Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else.     

A Perspective on the Accuracy of Economic Observations

In 1950 appeared the first edition of Oskar Morgenstern's Famous book, The Accuracy of Economic Observations. Nearly half a century later it is timely to return to Morgenstern's diagnosis and to contemplate his therapeutic recommendations. Morgenstern's vision can and should inform the consideration of the topic today because of the continued validity of many of his findings. His work still provides stimuli for studying the general problems of measurement, the varying requirements for accuracy, the issues of aggregate macroeconomic measures, and the prospects for economic and social measurement. This is so even if some of the bleaker assessments by Morgenstern, notwithstanding their technical merits, provide little or no practical guidance for statistical activities. In this context it is enlightening to recall the different practical attitudes adopted by Keynes and by some of his contemporaries in Germany regarding theoretical difficulties with aggregate macroeconomic data.