Linearity of regression for non-adjacent order statistics

Let X ₁,X ₂,…,X _n be a random sample from a continuous distribution with the corresponding order statistics X _1:n≤X _2:n≤…≤X _n:n. All the distributions for which E(X _{k+r: n}|X _k:n)=a X _k:n+b are identified, which solves the problem stated in Ferguson (1967). Received February 1998     

Estimation of the parameters of log-gamma distribution using order statistics

In this work we propose a technique of estimating the location parameter μ and scale parameter σ of log-gamma distribution by U-statistics constructed by taking best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to maximum likelihood estimators is also made.     

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.     

Mean residual life functions of finite mixtures,order statistics and coherent systems

We study properties of the mean residual life functions of finite mixtures. Specifically, we study ordering properties, monotonicity and the limiting behaviour. We show, under some mild conditions, that the limiting behaviour is similar to that of the strongest member (in the mean residual life order) of the mixture. We also consider the case of negative mixtures (i.e., mixtures with some negative coefficients) which is applied to study the behaviour of the mean residual life of order statistics and coherent systems with possibly dependent components. Partially Supported by Ministerio de Ciencia y Tecnologí a under grant BFM2003-02947 and Fundación Séneca under grant 00698/PI/04.     

汽车市场订单管理流程实施

论文探讨了汽车厂商订单管理流程的具体实施,分析了订单管理对区域市场经营模式和经销商能力提升的促进。随后,论文详细研究了订单管理流程中最为重要的年采购目标管理流程、月采购计划流程和周采购计划流程。     

Generalized densities of order statistics

Let X ₁, ... , X _n be independent identically distributed random variables with distribution F . We derive expressions for generalized joint 'densities' of order statistics of X ₁, ... , X _n , for arbitrary distributions F , in terms of Radon–Nikodym derivatives with respect to product measures based on F . We then give formulae for conditional distributions of order statistics and use them to derive results concerning Markov properties of order statistics, formulae for distributions of trimmed sums, and other useful representations. Our approach leads to simple and natural expressions which appear not to have been given before.     

Sharp bounds on moments of generalized order statistics

Sharp lower and upper bounds on expected values of generalized order statistics are proven by the use of rearranged Moriguti's inequality. The method yields improvements of known quantile and moment bounds for expectations of order and record statistics based on independent identically distributed random variables. The bounds are attainable providing new characterizations of two-point distributions. Received: January 1999     

融资优序与行业管制——兼析中国上市公司“异常融资优序”现象

企业融资先通过内部资金进行,然后再通过银行借款或发行低风险的债券,最后才采用股票,这种融资的“先后顺序”是企业出于降低融资成本和防止剩余利润被分享所做出的理性选择,这就是融资优序理论。本文认为,寡头竞争所形成的行业进入壁垒为优序融资的实现提供了必须的市场环境,其资金使用方式能够优化资源配置,提高资金的使用效率。融资优序理论在发达市场经济国家得到了实践的验证,但在我国上市公司中却存在“异常融资优序”(Abnormal pccking Order)现象,即外部资金优于内部资金,外部资金中股权融资优于债权融资。其原因在于,中国市场经济不太完善,缺乏通过寡头竞争自发形成的行业进入壁垒。本文认为只有采取行业管制手段,设置一定的行业进入壁垒,才能实现优序融资,从而达到优化资源配置的目的。     

A characterization of exponential distributions based on order statistics

This note contains a characterization of exponential distributions based on the properties of linear transformations of order statistics. This is a certain converse of a well known theorem of Rényi about the distribution of linear combinations of order statistics from exponential distributions. Some statistical applications of the result are indicated.     

Lagged order flows and returns: A longer-term perspective

In this paper, we consider the large-sample relation between returns and lagged order flows over horizons of up to 2 months. The analysis is motivated by work in market microstructure which suggests that the effects of inventory control on stock returns should be discernible over horizons longer than those considered in the literature. We begin our analysis by developing a simple model of inventory effects in the presence of public information. Using mid-quote return data, we then find some evidence of return predictability using order flows, even after controlling for lagged returns, which is consistent with our theoretical setting. The relation is present only for negative imbalances and is stronger in large firms rather than small ones. Overall, the analysis is consistent with the notion that inventory control effects span several weeks.     

The equivalence of the bishop-de leeuw and the pigou dalton order structures of measures

In this paper it is shown that the Bishop-de Leeuw and the Pigou-Dalton order structures of measures are the same.

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Riassunto In questo lavoro viene dimostrato, che le structture d’ordine per le misure di Bishop-de Leeuw e di Pigou-Dalton si equivalgono.

     

Do foreign institutions outperform in the Taiwan options market?

This paper investigates comparative information advantage for foreign and domestic institutions on Taiwan's index options by examining the intraday information content of limit orders placed by foreign and domestic institutions, respectively. The height and length of limit order book provided by either foreign or domestic institutions exhibit predictive power on subsequent price changes in options, especially for put options. The information advantage is more significant for foreign institutions with respect to both call and put options. On the other hand, the results are mixed when order imbalance is used as the proxy of information on limit order book. Foreign institutions outperform domestic institutions for put options, not call options. Order imbalance, ignoring differential aggressiveness of limit orders, fails to capture comparative information advantage for foreign institutions. The superior information advantage for foreign institutions persists during the financial tsunami of 2008–2009 and periods of substantial price changes.     

Distributions determined by conditioning on a pair of order statistics

LetX ₁,X ₂, ...,X _n (n≥3) be a random sample on a random variableX with distribution functionF having a unique continuous inverseF ⁻¹ over (a,b), −∞≤a<b≤∞ the support ofF. LetX _1:n <X _2:n <...<X _n:n be the corresponding order statistics. Letg be a nonconstant continuous function over (a,b). Then for some functionG over (a, b) and for some positive integersr ands, 1<r+1<s≤n

Estimating survivor function using optimally selected order statistics

This paper deals with the estimation of survivor function using optimally selected order statistics when the sample sizen is large. We use the estimates (μ*,σ*) based on the optimum set of order statistics for largen and fixedk (≤n) such that the estimate has optimum variance property. The asymptotic relative efficiency of such an estimator is compared with the one based on the complete sample. The general theory of the problem and specific details with respect to a two-parameter Normal, Logistic, Exponential and Pareto distributions is considered as an example.     

Predicting the sample mean by extreme order statistics

Summary This paper considers the prediction of the sample mean by extreme order statistics when the population distribution is known. The predictor and its mean square error are found. The problem is studied in details for the normal model.     

Tail index estimation based on linear combinations of intermediate order statistics

Based on linear combinations of intermediate order statistics, we introduce a new class of estimators for the exponent of a distribution function F with a regularly varying upper tail. We prove asymptotic normality and we make a comparison with existing proposals using the mean squared error as criterion.     

Sharp exponential and entropy bounds on expectations of generalized order statistics

Sharp lower and upper bounds on expected values of generalized order statistics are proven by the use of Moriguti's inequality combined with the Young inequality. The bounds are expressed in terms of exponential moments or entropy. They are attainable providing new characterizations of some nontrivial distributions. Received October 2001/Revised May 2002     

Bounds on expectations of small order statistics from decreasing density populations

For i > (n + 1)/2, Danielak (Statistics 37:305–324, 2003) established an optimal positive upper mean-variance bound on the expectation of ith order statistic based on the i.i.d. sample of size n from the decreasing density population. We show that the best bounds on the expected deviation of the ith order statistics from the population mean, i ≤ (n + 1)/2, expressed in more general scale units generated by pth absolute central moments with p > 1 amount to zero. We also determine the respective strictly negative bounds in the mean absolute deviation units.