Ein allgemeines Konstruktionsverfahren für Konfidenzbereiche

Summary A theorem ofTakács concerning interchangeable random variables is used to derive a simple method for the construction of confidence regions. Applying this method to a location parametera we get a.s. convergence of the confidence interval toa if the sample sizen increases while its probability is (n–1)/(n+1). Under certain conditions the interval contains always the maximum-likelihood estimate and another estimate which results from a least squares postulate. Lower bounds are given for the probability that our intervals become shorter than the intervals we would get relying on the central limit theorem. In order to avoid an assumption of finite support needed first to derive the a.s. convergence, we modify our method omitting extreme values.The modified intervals converge forn with probability 1 to the true parameter value under weaker conditions. A lower bound for the probability and-using a result due toRényi-theasymptotic probability of the modified interval is given. For the two kinds of intervals a formula concerning the velocity of their convergence to the length 0 is derived.Finally, the results are extended to a shift parameter in the two-sample case. Here we derive for equal sample sizes the exact probability of the modified interval and give upper and lower bounds fir its asymptotic probability. The method is practicable also if one sample size is an integer multiple of the other.     

Christofides’ randomized response technique in complex sample surveys

Christofides (2003) has given an improved modification of Warners (1965) pioneering randomized response (RR) technique in estimating an unknown proportion of people bearing a sensitive characteristic in a given community. As both these RR devices are shown to yield unbiased estimators based only on simple random sampling (SRS) with replacement (WR) but in practice samples are mostly taken with unequal selection probabilities without replacement (WOR), here we present methods of estimation when Christofides RR data are available from unequal probability samples. Warners (1965) RR device was earlier shown by Chaudhuri (2001) to be applicable in complex surveys. For completeness we present estimators for the variance of our estimator and also describe what to do if some people opt to divulge truths.This research is partially supported by CSIR grant No. 21(0539)/02/EMR-II     

Application of one‐step method to parameter estimation in ODE models

In this paper, we study application of Le Cam's one‐step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one‐step method starts from a preliminary ‐consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n →∞ ) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one‐step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary ‐consistent estimator that we use depends on non‐parametric smoothing, and we provide a data‐driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one‐step method for practical use is pointed out.     

The restricted regularity of admissible minimax criteria for many well known parametric statistical problems

Summary The stability of test selection criteria is a question that was raised byLeCam in 1964 [seeLeCam, 1964], but which seems to have received very little subsequent attention. Roughly, the problem posed byLeCam was to decide whether a given criterion is regular at a given statistical problem, i.e. given that the criterion prescribes the test ₀ for the statistical problem, (₀,D ₀,R ₀), whether it prescribes a best which is nearly the same as ₀ for any statistical problem, (, D,R), near to (₀, D₀,R ₀).A more precise formulation ofLeCam's question is one of the objectives of this paper. This involves defining a suitable topology on the domain of problems where the criterion in question is to be applied. Elementary minimax results of a general nature are proved, and counter examples are given to show that the assumptions used are not completely superfluous. The generality of these results seems to lend support to the authors opinion, that the method of formulation is suitable for treating minimax questions. We then consider the standard elementary problems of parametric statistics, (monotone likelihood ratio, general exponential family) and prove that the admissible minimax criterion is regular with respect to certain types of perturbations in these problems. The treatment is, in a sense, restricted and departs fromLeCam in holding the risk function essentially constant while varying the parameter space. That the problem variations considered may be of some practical interest and that the general formulations used are not completely unrealistic is shown at the conclusion of the paper where we apply a rest, icted regularity theorem to obtain regularity results for the binomial case.     

Foreign trade in the kaleckian perspective plan

In Kalecki's outline for a perspective plan a distinction is drawn between demand-determined and supply-constrained industries. Foreign trade operates on a vent-for-surplus principle whereby supply industries are run at full capacity and excess supplies (demands) are exported (imported). This policy is assessed using a simple two-sector model and is given only qualified support. Modifications to his plan procedure are accordingly suggested.     

The “Good Cause Norm” in Employment Relations: Empirical Evidence and Policy Implications

Critics of the American employment at-will doctrine have argued that it should be abandoned because it is at odds with a societal level norm that employees should only be discharged for good reasons (the good cause norm). This paper examines the extent to which there is conceptual and empirical support for the existence of such a norm. Theoretical perspectives supporting the norms existence are discussed and integrated, and an interdisciplinary review of relevant research is provided. In light of the support that is found for the existence of a good cause norm in the American workplace, it is proposed that the current employment at-will default rule be changed to a waivable employee right to be discharged for good cause only.     

Increase in Precision when Estimating Parameters in Computer Assisted Testing Using Response Time

A model is given in this article that associates response time to each item with its relative difficulty for the person examined. The properties of the model are presented with respect to the quantity of information, while deducing the parameter estimators. Likewise, an empirical study to prove the feasibility and plausibility of the model is carried out, feasibility being understood as the existence of adequate estimators for the parameters of the model and plausibility the adjustment of the model proposed to the items in a spatial aptitude test used to demonstrate this (Rotation of solid figures). For this, the model is tested with simulated data, comparing the behaviour of the estimates carried out on the model proposed with the estimates made by a programme such as BILOG-MG. It is shown that, with the exception of parameter c (pseudo-chance) which does not benefit from the inclusion of the response time, the estimates for the model are always higher for parameters a (discrimination) and b (difficulty) of the items, always giving rise to a higher correlation with the original data, in spite of the inefficiency of the computation algorithm employed. The results suggest that the use of response time supplies as much information or more than the use of very informative a priori distributions.     

Estimation of the regression slope by means of Gini’s cograduation index

The simple linear model \(Y_i = \alpha + \beta \, x_i + \epsilon _i\) \((i=1,2, \ldots ,N \ge 2)\) is considered, where the \(x_i\)’s are given constants and \(\epsilon _1, \epsilon _2 , \ldots , \epsilon _N\) are independent identically distributed (iid) with continuous distribution function F. An estimator \(\tilde{\beta }\) of the slope parameter is proposed, based on a stochastic process which makes use of Gini’s cograduation index. The properties of \(\tilde{\beta }\) and of the related confidence interval are studied. Some comparisons are given, in terms of asymptotic relative efficiency, with other estimators of \(\beta \) including that obtained with the method of least squares.     

$$\mathcal{D}$$-optimal Minimum Support Mixture Designs in Blocks

An easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. The resulting designs are -optimal in the class of minimum support designs. It is illustrated that the minimum support designs are more efficient than orthogonally blocked mixture experiments presented in the literature and only slightly less efficient than -optimal designs.     

Estimation of the parameter of the inverse Gaussian distribution from generalised censored samples

In this paper, a new Type of censored sample referred as generalised censored sample is defined and is differentiated fromCohen's [1963] progressively censored type I and type II samples. The maximum likelihood estimate of the parameter of the inverse Gaussian distribution from generalised censored samples is obtained. An expression for the standard error of the estimate is given.     

Out of Welfare: Functioning of Income Support in Torino

This paper explores the opportunities provided by a file of longitudinal data regarding income support benefits for able bodied poor in order to understand the functioning of the local social assistance system in Torino. The features of this system, its selective-categorized character and the differences from universalistic systems are analyzed. In this framework, the duration of the periods users receive benefits has been studied by means of event history analysis. The probability of exit from welfare is related to socio-demographic characteristics of recipients. In particular we observe a lower propensity to exit for female headed households and households with children. The probability of exit appears to be affected also by labour market conditions, being higher when these are more favourable. The exit rate does not decrease as time elapsed in welfare moves on. We observe the existence of different styles of assistance among the different social services within the city. Difficulties related to the interpretation of the empirical results, given the selective-categorized features of the social assistance system, are emphasized. Finally, we discuss some theoretical issues about evaluation of income support policies.All the sections of this paper are the result of the cooperation of the authors. Nicola Negri has coordinated the various steps of the work and has written Section 5 with Contini. Nicoletta Bosco has mainly worked with Nicola Negri to prepare the data archive and has written Sections 2 and 3. Dalit Contini has discussed with Negri and Bosco the model of empirical analysis and has implemented it; she has written Sections 4 and 6. All authors share Section 1 and 7.     

Union Rules Intrude Upon the Nonunion Domain: Workplace Investigations and the NLRB

This paper examines the new legal landscape for nonunion employers who contemplate conducting investigations of alleged wrongdoing by their employees. The National Labor Relations Board (NLRB) has ruled that a certain right (the Weingarten right) previously guaranteed only to union members applies equally to at-will employees in nonunionized firms. As a result, all employees now possess the right to ask that a coworker be present during an investigatory interview. While the Weingarten right is sensible in a union environment, significant public policy and practical problems arise when this right is extended to the nonunion environment. This paper offers advice on managing the investigative process, given this new right, and it discusses the propriety of imposing union rules on the nonunion workplace.     

Nonparametric density estimates consistent of the order of <Emphasis Type="Italic">n</Emphasis><Superscript>−1/2</Superscript> in the <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–norm

We introduce an approximate minimum Kolmogorov distance density estimate of a probability density f₀ on the real line and study its rate of consistency for n. We define a degree of variations of a nonparametric family of densities containing the unknown f₀. If this degree is finite then the approximate minimum Kolmogorov distance estimate is consistent of the order of n^–1/2 in the L₁-norm and also in the expected L₁-norm. Comparisons with two other criteria leading to the same order of consistency are given.Received June 2002     

The bivariate non-central negative binomial distributions

Summary Four bivariate generalisations (Type I–IV) of the non-central negative binomial distribution (Ong/Lee) are considered. The Type I generalisation is constructed using the latent structure model scheme (Goodman) while the Type II generalisation arises from a variation of this scheme. The Type III generalisation is formed by using the method of random elements in common (Mardia). The Type IV is an extension of the Type I generalisation. Properties of these bivariate distributions including joint central and factorial moments are discussed; several recurrence formulae of the probabilities are given. An application to the childhood accident data of Mellinger et al. is considered with the precision of the Type I maximum likelihood estimates computed.     

Shrinkage estimation of <Emphasis Type="Italic">P</Emphasis>(<Emphasis Type="Italic">X</Emphasis><<Emphasis Type="Italic">Y</Emphasis>) in the exponential case with common location parameter

We consider the problem of estimating R=P(X<Y) where X and Y have independent exponential distributions with parameters and respectively and a common location parameter . Assuming that there is a prior guess or estimate R₀, we develop various shrinkage estimators of R that incorporate this prior information. The performance of the new estimators is investigated and compared with the maximum likelihood estimator using Monte Carlo methods. It is found that some of these estimators are very successful in taking advantage of the prior estimate available.Acknowledgments. The authors are grateful to the editor and to the referees for their constructive comments that resulted in a substantial improvement of the paper.     

Arbitrage and completeness in financial markets with given <Emphasis Type="Italic">N</Emphasis>-dimensional distributions

Abstract In this paper, we focus on the following problem: given a financial market, modelled by a process , and a family of probability measures on , with N a positive integer and the time space, we search for financially meaningful conditions which are equivalent to the existence and uniqueness of an equivalent (local) martingale measure (EMM) Q such that the price process S has under Q the pre-specified finite-dimensional distributions of order N (N-dds) . We call these two equivalent properties, respectively, N -mixed no free lunch and market N -completeness. They are based on a classification of contingent claims with respect to their path-dependence on S and on the related notion of N-mixed strategy. Finally, we apply this approach to the Black-Scholes model with jumps, by showing a uniqueness result for its equivalent martingale measures set. Mathematics Subject Classification (2000): 60G48, 91B28 Journal of Economic Literature Classification: G12, D52