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We study the limiting behaviour of the maximum of a bivariate (finite or infinite) moving average model, based on discrete random variables. We assume that the bivariate distribution of the iid innovations belong to the Anderson's class (Anderson, 1970). The innovations have an impact on the random variables of the INMA model by binomial thinning. We show that the limiting distribution of the bivariate maximum is also of Anderson's class, and that the components of the bivariate maximum are asymptotically independent. FCT - Fundação para a Ciência e a Tecnologia published

Hintergrund: Die Ergebnisqualitat von orthopadischen Eingriffen wie Hufttotalendoprothese (HTP) oder Knietotalendoprothese (KTP) wurde bisher mit der Veranderung der Mittelwerte von Fragebogenscores angegeben. Damit entsteht der Eindruck, dass alle eingeschlossenen Patienten eine Verbesserung erfahren. In Realitat zeigt sich bei 80–85 % der Patienten eine Reduktion der Beschwerden, die restlichen Patienten (1 von 6 Patienten) haben unveranderte oder mehr Beschwerden. Mit dem REPP-Wert (relativer Effekt pro Patient) lasst sich der individuelle Erfolg pro Patient berechnen. Dieser berechnet sich als Ausgangswert−Ergebniswert dividiert durch Ausgangswert. Der Wert betragt maximal 1 (beschwerdefrei in der Nachkontrolle), 0 bei keinem Effekt und Negativwert bei Verschlechterung. Die Zuordnung in eine Ergebnisgruppe hangt vom REPP-Wert ab: exzellent 0,95–1, gut 0,5–0,95, masig > 0,2–0,5, unverandert −0,2–0,2 und schlechter ≤ −0,2. Zusammen ergeben sich so 5 Ergebnisgruppen: exzellent, gut, masig, unverandert, schlechter. Patienten und Methode: Im lokalen Prothesenregister wurde die Ergebnisqualitat 1 Jahr nach Huft- und Knietotalprothese zwischen Marz 2003 und November 2008 mit Patientenfragebogen (WOMAC, EuroQoL) berechnet und die Erfolgsrate mit den REPP-Werten mit den „respondern“ nach OMERACT-OARSI–Kriterien verglichen. Eingeschlossen waren Patienten mit vollstandigen Datensatzen und einseitiger HTP/KTP. Ergebnisse: Ergebnisgruppen WOMAC-Fragebogen (HTP/KTP): exzellent 29/14 %, gut 51/54 %, masig 11/13 %, unverandert 5/12 %, schlechter 4/7 %. Ergebnisgruppen EuroQoL-Fragebogen (HTP/KTP): exzellent 16/6 %, gut 41/42 %, masig 25/28 %, unverandert 12/16 %, schlechter 6/8 %. Die Erfolgsraten nach HTP sind vergleichbar; nach REPP-Methode 91 % und nach OMERACT-OARSI-Kriterien 92 %. Schlussfolgerung: Die Berechnung der REPP-Werte und die Einteilung der Patienten in die Ergebnisgruppen sind einfach. Die Ergebnisgruppen sind abhangig vom Eingriff (HTP bessere Resultate als KTP) und vom verwendeten Patientenfragebogen (bessere Resultate mit einem spezifischen als mit einem generischen Fragebogen). Im Vergleich zur Veranderung der Mittelwerte sind die Ergebnisgruppen sowohl fur die Patienten als auch Orthopaden aussagekraftiger.

To evaluate the performance of a prototype membrane stent, MembraX, in the prevention of acute and late embolization and to quantify particle embolization during carotid stent placement in human carotid explants in a proof of concept study.Thirty human carotid cadaveric explants (mild stenoses 0-29%, n = 23; moderate stenoses 30-69%, n = 3; severe stenoses 70-99%, n = 2) that included the common, internal and external carotid arteries were integrated into a pulsatile-flow model. Three groups were formed according to the age of the donors (mean 58.8 years; sample SD 15.99 years) and randomized to three test groups: (I) MembraX, n = 9; (II) Xpert bare stent, n = 10; (III) Xpert bare stent with Emboshield protection device, n = 9. Emboli liberated during stent deployment (step A), post-dilatation (step B), and late embolization (step C) were measured in 100 microm effluent filters. When the Emboshield was used, embolus penetration was measured during placement (step D) and retrieval (step E). Late embolization was simulated by compressing the area of the stented vessel five times.Absolute numbers of particles (median;100 microm) caught in the effluent filter were: (I) MembraX: A = 7, B = 9, C = 3; (II) bare stent: A = 6.5, B = 6, C = 4.5; (III) bare stent and Emboshield: A = 7, B = 7, C.=.5, D = 8, E = 10. The data showed no statistical differences according to whether embolic load was analyzed by weight or mean particle size. When summing all procedural steps, the Emboshield caused the greatest load by weight (p = 0.011) and the largest number (p = 0.054) of particles.On the basis of these limited data neither a membrane stent nor a protection device showed significant advantages during ex vivo carotid angioplasty. However, the membrane stent seems to have the potential for reducing the emboli responsible for supposed late embolization, whereas more emboli were observed when using a protection device. Further studies are necessary and warranted.

To prove the effectiveness of a new stent concept with integrated protection (MembraX [MX]) by comparing it with five cerebral protection devices designed for carotid angioplasty in an in vitro model.Two simulation series of embolization from carotid angioplasty have been performed. In the first series, polyvinyl-alcohol particles (150-250 microm [small], 355-500 microm [medium], 710-1000 microm [large]; 5 mg each) were injected into a silicone flow model simulating the aortic arch with a carotid bifurcation. The particles were injected proximally to the partially deployed MX stent or one of the following protection devices: Angioguard (AG), FilterWire EX (EX), Trap, Neuroshield (NS), or GuardWire Plus (GW). Particles evading the protection device were caught in a filter at the end of the flow model and weighed. In the second series, human plaque material (8-12 particles; total weight 6.09 +/- 0.01 mg; 500-1500 microm) was injected into the model with the respective devices. MX was compared with the AG, EX, Trap, and NS devices.MX had the most effective overall filtration performance for polyvinyl alcohol particles in the effluent of the internal carotid artery (ICA; 0.43 mg, 2.9%), compared with NS (0.53 mg, 3.5%), GW (1.10 mg, 7.0%), EX and AG (1.18 and 1.21 mg, respectively; 7.8% and 8.0%), and Trap (1.24 mg, 8.2%). MX performed best for the small particles (2.0% passed particles into ICA; P.05 compared with all). Human plaque material was retained best in the in vitro model by MX (0.0%), followed by NS (0.8%), EX (1.3%), Trap (2.6%), and AG (4.4%).In vitro, none of the tested devices had the ability to prevent embolization completely. Comparing current designs, the MX device captured the highest percentage of the three different particle groups. Tested with human plaque emboli, MX performed effectively in filtering the particles in the ICA.

The Late Maunder Minimum (LMM; 1675-1715) delineates a period with marked climate variability within the Little Ice Age in Europe. Gridded monthly mean surface pressure fields were reconstructed for this period for the eastern North Atlantic-European region (25°W-30°E and 35-70°N). These were based on continuous information drawn from proxy and instrumental data taken from several European data sites. The data include indexed temperature and rainfall values, sea ice conditions from northern Iceland and the Western Baltic. In addition, limited instrumental data, such as air temperature from central England (CET) and Paris, reduced mean sea level pressure (SLP) at Paris, and monthly mean wind direction in the Oresund (Denmark) are used. The reconstructions are based on a canonical correlation analysis (CCA), with the standardized station data as predictors and the SLP pressure fields as predictand. The CCA-based model was performed using data from the twentieth century. The period 1901-1960 was used to calibrate the statistical model, and the remaining 30 years (1961-1990) for the validation of the reconstructed monthly pressure fields. Assuming stationarity of the statistical relationships, the calibrated CCA model was then used to predict the monthly LMM SLP fields. The verification results illustrated that the regression equations developed for the majority of grid points contain good predictive skill. Nevertheless, there are seasonal and geographical limitations for which valid spatial SLP patterns can be reconstructed. Backward elimination techniques indicated that Paris station air pressure and temperature, CET, and the wind direction in the Oresund are the most important predictors, together sharing more than 65% of the total variance. The reconstructions are compared with additional data and subjectively reconstructed monthly pressure charts for the years 1675-1704. It is shown that there are differences between the two approaches. However, for extreme years the reconstructions are in good agreement.

AIM The visual analogue scale (VAS) and Likert scale (LS) are widely used but the patients might have difficulties to work with these scales and there might be errors in calculation. The visual circle scale (VCS) is a graphic construct with a simple grading to augment the understanding and ease for calculation. METHOD This study compares the different scales in orthopaedic patients for pain assessment postoperatively. In addition, the scales were rated by the patients for simplicity, understanding and global rating. RESULTS Included were 65 patients (40 women) with an average age of 66 years with 330 pain assessments and 65 questionnaire ratings. The average pain was LS 42.7, VAS 39.3, VCS 44. The correlation coefficients r (Spearman) between all scales were > 0.89 and the same held also for sensitivity for change. The VCS was the scale preferred by > 50 % of the orthopaedic patients to assess the pain. CONCLUSION The VCS is able to measure pain comparably to the known scales (VAS, Likert scale). From the patients point of view it is the preferred scale to work with.

This paper provides bounds and approximations for the distribution of the maximum queue length for M/M/s queues, based on an asymptotic analysis involving the extremal index. These results are compared to those by Anderson [1], Serfozo [6] and McCormick and Park [3]

The outcome of orthopaedic surgery such as total hip replacement (THR) or total knee replacement (TKR) is commonly given by the change in mean scores on patient-reported outcome measures (Prom's). This may give the impression that all enrolled patients have experienced an improvement. But the Swedish hip registry and other studies report a reduction of complaints in 80-85 % of patients ("responders"), with the remainder (approximately one in six) remaining unchanged or reporting worse complaints ("non-responders"). According to Cohen, the degree of success in the "responders" group can be subdivided into excellent, good and moderate. For a given treatment, a total of 5 different outcome groups can therefore be defined: excellent, good, moderate, unchanged and worse. Allocation to the groups is based on the "relative effect per patient" (REPP). The REPP is calculated as the base-line score minus the post-treatment score divided by the baseline score. The maximum possible REPP is 1; a REPP of 0 means no effect and a negative REPP means deterioration. Allocation to the outcome groups is as follows: excellent 0.95 to 1 REPP, good 0.5 to 0.95 REPP, moderate over 0.2 to 0.5 REPP, unchanged -0.2 to 0.2 REPP and worse below -0.2 REPP.Our local arthroplasty register was used to evaluate the 1-year outcomes of THR and TKR patients operated between March 2003 and November 2008, using WOMAC scores and EuroQoL scores. Only patients with complete data sets and unilateral THR/TKR were included. The success rate given by the REPP method was compared with that of the "responder rate" method defined by the OMERACT-OARSI criteria.With the WOMAC questionnaire, outcomes were as follows (THR/TKR): excellent 29/14 %, good 51/54 %, moderate 11/13 %, unchanged at 5/12 %, worse 4/7 %. The corresponding values for the EuroQoL were (THR/TKR): excellent 16/6 %, good 41/42 %, moderate 25/28 %, unchanged 12/16 %, worse 6/8 %. For THR, success rates were 92 % using the "responder rate" method (OMERACT-OARSI criteria) and 91 % using the REPP method with the WOMAC.Calculation of the REPP and the subsequent allocation to outcome groups is simple. The distribution of outcomes depends on the intervention (THR results better than TKR) and the patient questionnaire used (better results with a condition-specific than a generic questionnaire). The proportion of "unchanged" and "moderate" outcomes was greater with the generic questionnaire than with the condition-specific questionnaire, while the proportion of "worse" outcomes was similar for the two instruments. Partitioning of the degree of success into sub-groups, based on the REPP, provides more information for both the patient and the orthopaedic surgeon.

We discuss the limits of point processes which are generated by a triangular array of rare events. Such point processes are motivated by the exceedances of a high boundary by a random sequence since exceedances are rare events in this case. This application relates the problem to extreme value theory from where the method is used to treat the asymptotic approximation of these point processes. The presented general approach extends, unifies and clarifies some of the various conditions used in the extreme value theory.

Exceedances of a non-stationary sequence above a boundary define certain point processes, which converge in distribution under mild mixing conditions to Poisson processes. We investigate necessary and sufficient conditions for the convergence of the point process of exceedances, the point process of upcrossings and the point process of clusters of exceedances. Smooth regularity conditions, as smooth oscillation of the non-stationary sequence, imply that these point processes converge to the same Poisson process. Since exceedances are asymptotically rare, the results are extended to triangular arrays of rare events.

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

The paper considers the problem of finding the distribution of the rate of return on an investment when the cash flow is described by a Gaussian process. The question is formulated in terms of the first zero of what is called the rate of return process. An explicit solution is generally not available and methods previously used by the authors in another context are applied to obtain an approximation. The arguments apply to locally stationary Gaussian processes as introduced by Berman (1974).

We consider the convex hull of a sample of n randomly placed points in a unit circle. Obviously not all of the n points are needed to construct the convex hull. We show that asymptotically only the points belonging to a certain ring are used for the convex hull, where the size of the ring decreases at a certain rate such that the error of not completely correct construction of the convex hull by the particular subset of points tends to 0.

This paper deals with the development of a 4 degree of freedom direct drive master manipulator system which has the ability of virtually adjusting its mechanical impedance. In the field of bilateral master-slave manipulation, there are some important points to be considered when a master manipulator is designed. One point is related to how to measure the human operator’s arm motion with high accuracy (which the operator produces to teach the trajectory of tasks). Another point is how to design an effective force/torque generator to make an operator feel the constraint forces the slave arm will receive from the environments during tasks. To satisfy these requirements, a manipulator with a variable mechanical impedance structure and joints equipped with high resolution angular displacement sensors is expected to be developed. The use of the variable impedance structure provides a capability of reflecting the constraint forces to an operator not only statically, but also dynamically. This is effective to present the constraints to an operator with high fidelity. In the research, joint mechanisms and joint sensors suitable for the impedance control were discussed, while the mechanical structure of the master manipulator which is effective to construct a simple impedance control law was investigated. With these considerations in mind, a master manipulator was designed and its impedance control law was formulated. The features of the manufactured manipulator are summarized as follows; (1) each joint is driven by a direct drive torque motor with less friction and has a high resolution angular encoder attached to a processor which can provide joint angular displacement, angular velocity and angular acceleration. (2) the manipulator has the decoupled and configuration-invariant inertia structure in part which is effective to simplify impedance control law. In the paper, the design concept of the master manipulator is first discussed. Secondly, the details of the manufactured manipulator structure are explained. Finally, the results of the evaluation experiments are described and the fundamental characteristics of the system are confirmed.

The visual analogue scale (VAS) and Likert scale (LS) are widely used but the patients might have difficulties to work with these scales and there might be errors in calculation. The visual circle scale (VCS) is a graphic construct with a simple grading to augment the understanding and ease for calculation.This study compares the different scales in orthopaedic patients for pain assessment postoperatively. In addition, the scales were rated by the patients for simplicity, understanding and global rating.Included were 65 patients (40 women) with an average age of 66 years with 330 pain assessments and 65 questionnaire ratings. The average pain was LS 42.7, VAS 39.3, VCS 44. The correlation coefficients r (Spearman) between all scales were0.89 and the same held also for sensitivity for change. The VCS was the scale preferred by50 % of the orthopaedic patients to assess the pain.The VCS is able to measure pain comparably to the known scales (VAS, Likert scale). From the patients point of view it is the preferred scale to work with.

In healthy subjects and patients with bleeding peptic ulcers, ranitidine and omeprazole, given parenterally, achieve high intragastric pH values on the first day of therapy. However, data on the antisecretory effect beyond the first 24 h is scanty. In addition, the superiority of either infusion or injection of omeprazole remains unproven. Thus, we have compared the antisecretory effect of high dose omeprazole and ranitidine infusion and injection over the critical first 72 h.A total of 34 healthy volunteers were randomized into a double-blind crossover 72 h intragastric pH-metry study (data compared: median pH, percentage of time with pH4 and pH6). Omeprazole-infusion: initial bolus of 80 mg + 8 mg/h; omeprazole-injection: initial bolus of 80 mg + 40 mg/6 h; Ranitidine-infusion: initial bolus of 50 mg + 0.25 mg/kg/h; ranitidine-injection: 100 mg/6 h.Omeprazole-infusion versus ranitidine-infusion: on day 1: median pH 6.1 vs 5.1 (p = 0.01) and 95% vs 70% was pH4 (p0.01); on day 2: median pH 6.2 vs 3.2 (p0.01); and 100% vs 38% was pH4 (p0.01); on day 3: median pH 6.3 vs 2.7 (p0.01); 100% vs 26% was pH4 (p0.01). Injections of both drugs were significantly less effective than the infusions on day 1. Thereafter, omeprazole injection was almost as effective as omeprazole infusion, whereas ranitidine injection and infusion were equally effective.Our study shows, for the first time, that omeprazole infusion was significantly superior to all other regimens by having a high median pH6 on each day. The tolerance effect of ranitidine, however, led to a rapid loss of antisecretory activity on days 2 and 3, rendering it inappropriate for situations in which high intragastric pH-levels appear to be essential.

Background—Malignant colorectal polyps are defined as endoscopically removed polyps with cancerous tissue which has invaded the submucosa. Various histological criteria exist for managing these patients.Aims—To determine the significance of histological findings of patients with malignant polyps.Methods—Five pathologists reviewed the specimens of 85 patients initially diagnosed with malignant polyps. High risk malignant polyps were defined as having one of the following: incomplete polypectomy, a margin not clearly cancer-free, lymphatic or venous invasion, or grade III carcinoma. Adverse outcome was defined as residual cancer in a resection specimen and local or metastatic recurrence in the follow up period (mean 67 months).Results—Malignant polyps were confirmed in 70 cases. In the 32 low risk malignant polyps, no adverse outcomes occurred; 16 (42%) of the 38 patients with high risk polyps had adverse outcomes (pConclusion—As no patients with low risk malignant polyps had adverse outcomes, polypectomy alone seems sufficient for these cases. In the high risk group, surgery is recommended when either of the two independent risk factors, incomplete polypectomy or a resection margin not clearly cancer-free, is present or if there is a combination of other risk factors. As lymphatic or venous invasion or grade III cancer did not have an adverse outcome when the sole risk factor, operations in such cases should be individually assessed on the basis of surgical risk.

Symptoms of functional dyspepsia are common and patients often self-medicate with antacids, or with low-dose H2-antagonists which are available as over-the-counter medications. To date, there has been limited information available comparing the effects on intragastric acidity of these two types of over-the-counter medication. Therefore we studied the effect of the antacid Rennie and two H2-antagonists on the intragastric pH of fasting volunteers.Sixteen healthy, fasting volunteers were randomized into a double-blind, placebo-controlled, four-way crossover study comparing Rennie (calcium-magnesium carbonate) 1360 mg, ranitidine 75 mg, famotidine 10 mg and placebo. Their effect on gastric pH was monitored by a 4-h gastric pH-metry. The primary efficacy parameter was the time lag before an intragastric pH3.0 was reached after drug administration.The median time lag before pH3.0 was reached after drug administration was 5.8 min for Rennie, 64.9 min for ranitidine, 70.1 min for famotidine and 240.0 min for placebo. The percentage of time with values of pH3.0 was 10.4% for Rennie, 61.4% for ranitidine, 56.6% for famotidine and 1.4% for placebo.The onset of action in fasting volunteers was significantly faster with the antacid than with the two H2-antagonists. The duration of action was significantly longer with an H2-antagonist than with the antacid. This suggests that the two products should be used for different indications: antacids are superior for rapid pain relief, whereas H2-antagonists might be better for symptom prophylaxis--for example for nocturnal dyspepsia.

Control of ferce in the hand requires the synergistic co-operation of many intrinsic and extrinsic finger muscles (Maier, Hepp-Reymond & Meyer, 1991; Maier, 1992). An area of interest lies in the coordination and neuronal circuitry of the muscles involved, both at the global and at the motor unit (MU) level. Recent studies of MU synchronisation, found within and between muscles (Bremner, Baker & Stephens, 1991; Nordstrom, Fuglevand & Enoka, 1992; Schmied, Ivarsson & Fetz, 1993), have resulted in a better understanding of motoneuronal connectivity. The purpose of this investigation was to determine whether intra- and intermuscular (IAM, IRM) synchronisation is present between MUs in activated finger muscles in the precision grip and how it might be related to muscle synergies.

Neuronal activity was recorded in the ventral premotor cortex of one monkey (Macaca fascicularis) trained to exert finely graded forces with thumb and index finger on a force sensor in a visuomotor step-tracking paradigm. Trials with two or three consecutive ramp-and-hold force steps were presented randomly. Most neurons displayed similar discharge patterns in the two- and three-step trials and were assigned to one of the following classes: phasic, phasic–tonic, tonic, decreasing, and mixed. For more than 50% of the neurons with tonic activity, positive or negative correlations between firing rate and force were statistically significant. The indices of force sensitivity were on average higher for the two-step than for the three-step trials, indicating that the correlations yielded linearity over only a limited force range. The force-related cells were located in two regions of the ventral premotor cortex. One group was lying rostrally within the inferior limb of the arcuate sulcus, from which microstimulation elicited movements of fingers and hand. In the other more caudal region, adjacent to the finger region of primary motor cortex, microstimulation was rarely effective, but all neurons had clear peripheral receptive fields on finger and hand. The data indicate that two populations of neurons, located in the ventral premotor cortex, are related to movement execution. Effective microstimulation also suggests that one of the populations has fairly direct access to the spinal motor apparatus.Key words: precision grip, isometric force, premotor cortex, alert monkey, single cell activity.

The reliability of the dope control, of the chemical analysis of the urine probes in the accredited laboratories and their decisions, is discussed using probabilistic and statistical methods. Basically, we evaluated and estimated the positive predictive value which means the probability that an urine probe contains prohibited dope substances given a positive test decision. Since there are not statistical data and evidence for some important quantities in relation to the predictive value, an exact evaluation is not possible, only conservative, lower bounds can be given. We found that the predictive value is at least 90% or 95% with respect to the analysis and decision based on the A-probe only, and at least 99% with respect to both A- and B-probes. A more realistic observation, but without sufficient statistical confidence, points to the fact that the true predictive value is significantly larger than these lower estimates.

Following GRIZZLE (1965) and JESDINSKY et al. (1981) it is suggested to replace the traditional two-groups (AB, BA) crossover design by a four-groups (AA, AB, BA, BB) design in order to control for treatment-period interactions (carry-over effects). Contrary to the above authors it is proposed to use the increments D = X2 - X1 from 1 st to 2 nd observations rather than the observations themselves as the dependent variable. Testing for main- and interaction effects of treatment is treated for increment modified Grizzle- and Jesdinsky ANOVA models. Alternative and conditional tests are discussed. Numerical evaluations are illustrated by an example from psychopharmacology.

The strong law of large numbers for independent and identically distributed random variablesX i ,i=1, 2, 3,... with finite expectationE|X 1| can be stated as, for any ɛ>0, the number of integersn such that\(|n^{ - 1} \mathop {\mathop \sum \limits_{i \le n} }\limits^n X_i ---EX_1 | > \varepsilon \),N ɛ is finite a. s. It is known thatEN ɛ \varepsilon \) andE N 1 2 =∞.

Let (A, ≤) be a partially ordered set, {Xα} a collection of i. i. d. random variables, indexed byA. Let\(S_\alpha = \sum _{\beta \leqslant \alpha } X_\beta \), |α|=card {β∈A, β∈α}. We study the convergence rates ofSα/|α|. We derive for a large class of partially ordered sets theorems, like the following one: For suitabler, t with 1/2< 0, where\(M(x) = \sum _{j< x} d(j)\) withd(j)=card {α∈A, |α|=j}.

Place n arcs of equal length an uniformly at random on the circumference of a circle. We discuss the limiting distributions of the number of gaps, the length of the maximum gap and the uncovered proportion of the circle, depending on the asymptotic behaviour of an → 0.

Place n arcs of equal length a uniformly at random on the circumference of a circle. We discuss the joint limit distributions of the number of gaps, the uncovered proportion of the circle and the lengths of the largest gap and of the smallest gap, depending on how a → 0 as n →∞. We show that the results may be proved in a unified and simple way by using a result of Le Cam.

New simple estimators for the parameters of the extreme-value distribution, for use with censored data, are presented and are shown to have higher efficiency, in the case of light censoring (.8 ≤ r/n < 1.0), than previous simple estimators given by Engelhardt and Bain (1973, 1974) and Mann and Fertig (1975). Confidence intervals and significance tests based on these new estimators can also be obtained.

SUMMARY Consider the coverage of a k-dimensional unit cube by n spheres randomly placed according to a density f. Assume that f is non-uniform, having a unique interior minimum point m in the unit cube with f(m) = 0. We present necessary and sufficient conditions such that the probability that the unit cube is covered at least l times converges to 1 as n ∞. These conditions depend on the local behaviour of f in the neighbourhood of m and the radii δ of the random spheres.

We discuss conditions which characterize the limit distributions of multivariate extreme values in general nonstationary sequences of random vectors. We deal mainly with results such that the limit distributions can be found easily with the use of certain asymptotic independence properties. This paper extends known results for multivariate Gaussian sequences to non-Gaussian ones.

„In adaptive statistical inference, we use the sample to help us select the appropriate type of statistical procedure needed for the situation under consideration“. Mit diesen Worten beginnt R. Hogg seinen Artikel uber adaptive Methoden in der Encyclopedia of Statistical Sciences. Damit wird eine intuitiv leicht verstandliche Methode gemeint, die eine von Hogg propagierte Verbesserung der statistischen Verfahren erbringt. Es wird unsere Aufgabe sein, die „marktschreierischen“ (Tukey) adaptiven Verfahren mit den bekannten nicht-adaptiven statistischen, Methoden zu vergleichen. Als nicht-adaptiv betrachten wir die robusten Methoden und die Ausreisser-Verfahren. Allen drei genannten Methoden ist die Betrachtungsweise gemeinsam, sich gegen starke Abweichungen vom klassischen Normalverteilungsmodell abzusichern. Unter starken Abweichungen verstehen wir Modellverteilungen, die entgegen der Normalverteilung etwa nicht symmetrisch sind oder wesentlich starkere oder schwachere Tails aufweisen. Wir werden in den folgenden Vergleichen auch parametrische Methoden miteinbeziehen.

We show that the simple characterizations given by Takahashi for the independence and the total dependence of a multivariate extreme value distribution do not hold for the larger class of maximum infinitely divisible (max i.d.) distributions. This holds also for sup self-decomposable distributions.