A dynamic measure of inaccuracy between two past lifetime distributions

In the present communication we introduce a dynamic measure of inaccuracy between two past lifetime distributions over the interval (0, t). Based on proportional reversed hazard rate model (PRHRM), a characterization problem for this dynamic inaccuracy measure has been studied. An upper bound to the dynamic measure of inaccuracy H*(f, g; t) has also been derived.     

Entropy of type (α, β) and other generalized measures in information theory

Two types of generalizations ofChaundy andMcLeod's functional equation have been proposed in the paper. One generalization includes parameters and leads to a new measure of entropy, which includesDaroczy's entropy of type as a particular case. Such a generalization for functions of two variables leads to new quantities whose particular cases areKullback's information andKerridge's inaccuracy.The second generalization is obtained by adding a symmetric term multiplied by a constant and gives alternative characterizations of quantities studied earlier.     

Refining the workhorse oil market model

The Kilian and Murphy (Journal of Applied Econometrics, 2014, 29, 454–478) structural vector autoregressive model has become the workhorse model for the analysis of oil markets. I explore various refinements and extensions of this model, including the effects of (1) correcting an error in the measure of global real economic activity, (2) explicitly incorporating narrative sign restrictions into the estimation, (3) relaxing the upper bound on the impact price elasticity of oil supply, (4) evaluating the implied posterior distribution of the structural models, and (5) extending the sample. I demonstrate that the substantive conclusions of Kilian and Murphy (2014) are largely unaffected by these changes.     

Improved forecasting of autoregressive series by weighted least squares approximate REML estimation

Restricted maximum likelihood (REML) estimation has recently been shown to provide less biased estimates in autoregressive series. A simple weighted least squares approximate REML procedure has been developed that is particularly useful for vector autoregressive processes. Here, we compare the forecasts of such processes using both the standard ordinary least squares (OLS) estimates and the new approximate REML estimates. Forecasts based on the approximate REML estimates are found to provide a significant improvement over those obtained using the standard OLS estimates.     

A Biased Valuation: The Treatment of a Professional Degree in Divorce Actions

A bstract Over the past two decades, courts have unsuccessfully attempted to develop a consistent approach to the treatments of a professional degree in divorce actions. After reviewing the conceptual issues involved, a measurement method is suggested which would provide the fact finder with both an upper and a lower bound for the value of a degree. Hypothetical future income streams for average lawyers and physicians, and their spouses, are used to examine the impact of basing property settlements upon each of these bounds. It is argued that both equityand conceptual considerations support the conclusion that past decisions have very often inappropriately failed to consider the upper bound in valuing a degree in divorce settlements.     

On the asymptotic behaviour of the Stringer bound1

The Stringer bound is a widely used nonparametric 100(1 -α)% upper confidence bound for the fraction of errors in an accounting population. This bound has been found in practice to be rather conservative, but no rigorous mathematical proof of the correctness of the Stringer bound as an upper confidence bound is known and also no counterexamples are available. In a pioneering paper Bickel (1992) has given some fixed sample support to the bound's conservatism together with an asymptotic expansion in probability of the Stringer bound, which has led to his claim of the asymptotic conservatism of the Stringer bound. In the present paper we obtain expansions of arbitrary order of the coefficients in the Stringer bound. As a consequence we obtain Bickel's asymptotic expansion with probability 1 and we show that the asymptotic conservatism holds for confidence levels 1 -α, with α∈ (0,1/2]. It means that in general also in a finite sampling situation the Stringer bound does not necessarily have the right confidence level. Based on our expansions we propose a modified Stringer bound which has asymptotically precisely the right nominal confidence level. Finally, we discuss other consequences of the expansions of the Stringer bound such as a central limit theorem, a law of the iterated logarithm and the functional versions of them.     

A residual inaccuracy measure based on the relevation transform

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.     

Jack-knifing the ratio and the product estimators in double sampling

Summary Almost unbiased ratio and product type estimators have been obtained with the help of the Jack-Knifing technique for simple random sampling in two phases. The mean square errors of the resulting estimators have been compared with those of the corresponding usual (biased) estimators and it has been found that they are approximately same. This study generalizes similar single sampling results ofDurbin [1959],Shukla [1976] and others.     

Measuring regional inequality: to weight or not to weight?

Measuring regional inequality: to weight or not to weight? Spatial Economic Analysis. When estimating regional inequality, many economists use inequality indices weighted by regions’ proportion of the national population. Although this approach is widespread, its adequacy has not received attention in the regional science literature. This paper proves that such an approach is conceptually inconsistent, yielding an estimate of interpersonal inequality among the whole population of the country rather than an estimate of regional inequality. Nevertheless, as a measure of interpersonal inequality, such an estimate is very rough (even misleading) and does not always have an intuitive interpretation. Moreover, population-weighted inequality indices do not meet the requirements for an adequate measure of inequality.     

A Lower Bound for the Centered <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-Discrepancy on Asymmetric Factorials and its Application

The role of uniformity measured by the centered L ₂-discrepancy (Hickernell 1998a) has been studied in fractional factorial designs. The issue of a lower bound for the centered L ₂-discrepancy is crucial in the construction of uniform designs. Fang and Mukerjee (2000) and Fang et al. (2002, 2003b) derived lower bounds for fractions of two- and three-level factorials. In this paper we report some new lower bounds for the centered L ₂-discrepancy for a set of asymmetric fraction factorials. Using these lower bounds helps to measure uniformity of a given design. In addition, as an application of these lower bounds, we propose a method to construct uniform designs or nearly uniform designs with asymmetric factorials.     

An upper bound for the correlation ratio of records

We obtain an upper bound for a measure of the performance of the least squares predictor of the jth record of a sequence of continuous i.i.d random variables as a function of the ith record. We show also that such bound is attainable, except for location and scale parameters, by exponential distributions. This work was supported in part by Ministerio de Educación y Ciencia through Grants PB96-1416-CO2-02 and HA 1997-0123.     

Bounding endogenous regressor coefficients using moment inequalities and generalized instruments

The main approach to deal with regressor endogeneity is instrumental variable estimator (IVE), where an instrumental variable (IV) m is required to be uncorrelated to the regression model error term u (COR(m,u)=0) and correlated to the endogenous regressor. If COR(m,u)≠0 is likely, then m gets discarded. But even when COR(m,u)≠0, often one has a good idea on the sign of COR(m,u). This article shows how to make use of the sign information on COR(m,u) to obtain an one‐sided bound on the endogenous regressor coefficient, calling m a ‘generalized instrument’ or ‘generalized instrumental variable (GIV)’. If there are two GIV's m₁ and m₂, then a two‐sided bound or an improved one‐sided bound can be obtained. Our approach is simple, needing only IVE; no non‐parametrics, nor any ‘tuning constants’. Specifically, the usual IVE is carried out, and the only necessary modification is that the estimate for the endogenous regressor coefficient is interpreted as a lower/upper bound depending on the prior notion on the sign of COR(m,u) and some estimable moment. A real data application is done to Korean household data with two or more children to illustrate our approach for the issue of child quantity–quality trade‐off.     

Expected market returns: SVIX,realized volatility,and the role of dividends

This note provides a replication of Martin's (Quarterly Journal of Economics, 2017, 132(1), 367–433) finding that the implied volatility measure SVIX predicts US stock market returns up to 12‐month horizons. I find that this result holds for both S&P 500 and CRSP market returns, regardless of whether returns include or exclude dividends. The predictability largely disappears after the SVIX index is replaced by an exponentially weighted moving average measure of realized volatility, suggesting that SVIX holds incremental forward‐looking information compared to realized volatility, despite the high correlation between the two volatility measures.     

Correcting Standard Errors in Two‐stage Estimation Procedures with Generated Regressands*

Feenstra and Hanson [NBER Working Paper No. 6052 (1997)] propose a procedure to correct the standard errors in a two‐stage regression with generated dependent variables. Their method has subsequently been used in two‐stage mandated wage models [Feenstra and Hanson, Quarterly Journal of Economics (1999) Vol. 114, pp. 907–940; Haskel and Slaughter, The Economic Journal (2001) Vol. 111, pp. 163–187; Review of International Economics (2003) Vol. 11, pp. 630–650] and for the estimation of the sector bias of skill‐biased technological change [Haskel and Slaughter, European Economic Review (2002) Vol. 46, pp. 1757–1783]. Unfortunately, the proposed correction is negatively biased (sometimes even resulting in negative estimated variances) and therefore leads to overestimation of the inferred significance. We present an unbiased correction procedure and apply it to the models reported by Feenstra and Hanson (1999) and Haskel and Slaughter (2002) .     

Some Properties of Past Entropy and their Applications

In the context of information theory, measure of uncertainty in past lifetime distribution has been proposed by Di Crescenzo and Longobardi (J Appl Probab 39:434–440, 2002). In this paper, we study some ordering and aging properties in terms of past entropy (based on past lifetime) and develop some characterization results. Some discrete distribution results are also addressed here.     

On the entropy and inaccuracy of similarly and oppositely ordered discrete probability distributions (I)

This note deals with the entropy and inaccuracy of similarly and oppositely ordered discrete probability distributions. The concept of inaccuracy range has also been introduced. In particular, the inacuracy of -Power distributions with respect to another distribution has been discussed in detail. It is shown that these inaccuracies are monotonically increasing function of \ for oppositely ordered distributions and decreasing function of for similarly ordered distributions.     

Bounds for the utility-indifference prices of non-traded assets in incomplete markets

Abstract We consider a special class of financial models with both traded and non-traded assets and show that the utility indifference (bid) price of a contingent claim on a non-traded asset is bounded above by the expectation under the minimal martingale measure. This bound also represents the marginal bid price for the claim. The key conclusion is that the bound and the marginal bid price are independent of both the utility function and initial wealth of the agent. Thus all utility maximising agents charge the same marginal price for the claim. This conclusion is in some sense the opposite conclusion to that of Hubalek and Schachermayer (2001), who show that any price is consistent with some equivalent martingale measure. Mathematics Subject Classification (2000): 91B28, 91B16, 60J70 Journal of Economic Literature Classification: G13     

Run length analysis of Shewhart charts applied to drifting processes under an integrative SPC/EPC model

Engineering Process Controllers (EPC) are frequently based on parametrized models. If process conditions change, the parameter estimates used by the controllers may become biased, and the quality characteristics will be affected. To detect such changes it is adequate to use Statistical Process Control (SPC) methods. The run length statistic is commonly used to describe the performance of an SPC chart. This paper develops approximations for the first two moments of the run length distribution of a one-sided Shewhart chart used to detect two types of process changes in a system that is regulated by a given EPC scheme: i) changes in the level parameter; ii) changes in the drift parameter. If the drift parameter shifts, it is further assumed that the form of the drift process changes from a linear trend under white noise (the in-control drift model) into a random walk with drift model. Two different approximations for the run length moments are presented and their accuracy is numerically analyzed. Received: August 1998     

On the information criterion for selecting regressors

Summary It has been asserted in the past that any Bayesian treatment of the model selection problem in regression using some form of continuous loss structure would always lead to using the largest possible model (Leamer 1979; Chow 1981). We show in this paper that, provided the distinction between the choice of a model and the estimation of its parameters is maintained, the Kullback-Leibler information measure can be used in a Bayesian context to derive a criterion which may lead to parsimony of parameters in regression analysis. The regression models are taken as restrictions of a general class of distributions which includes the truen-variate distribution of the variabley. Separate criteria for the cases of known and unknown variance ofy are obtained. In the limiting situation when prior opinions about the parameters are weak, these criteria reduce to special cases of the generalizedC _p and AIC criteria (Atkinson 1981). Relationship with other criteria is discussed.