Effect of outliers on the estimation of parameters

Summary The estimation of parameter in the type of distributionf(x)=b x ^{–1 /b} exp (–x ^b (/b),x>0, is considered, when several outliers of the type , ,r=1,2, ...,k, are present in the data. The estimates of as well as of 's are put in the closed form. Special cases, Weibull, Gamma and Exponential are considered for the case of single outlier. Actual estimates are calculated from the generated samples of size 2 and 3 for the Weibull and Exponential.     

A note on optimum spacing of observations from a continuous time simple Markov process

Summary Assume thatX() is a continuous time simple Markov process with a parameter . The problem is to choose observation points ₀ < ₁ <...<_T which provide with the maximum possible information on . Suppose that the observation points are equally spaced, that is, fort=1, ...,T, T, ;_t–_t–1 is constant. Then the optimum value fors is obtained.     

Realization of closed,convex, and symmetric subsets of the unit square as regions of risk for testing simple hypotheses

It is well-known that the region of risk for testing simple hypotheses is some closed, convex, and (1/2, 1/2)-symmetric subset of the unit square, which contains the points (0, 0) and (1, 1). It is shown that for any such subsetR of the unit square and any atomless probability measureP on some -algebra there exists some probability measureQ on the same -algebra such thatR is the corresponding region of risk for testingP againstQ. This generalizes a result of [4] and is as a first step derived here for the special case, whereP is equal to the uniform distribution on the unit interval. The corresponding distributionQ is given explicitly in this case and the general case is treated by some well-known measure-isomorphism. This method of proof shows thatQ might be chosen to be of typeQ=Q ₁+(1–)Q ₂ for some satisfying 01, whereQ ₁ is a probability measure, which is absolutely continuous with respect toP andQ ₂ is a one-point mass.     

Interviewers,Interviewer Continuity,and Panel Survey Nonresponse

It is widely known that in practice, different interviewers have different response rates, though there has been no systematic examination of whether this is because of differences among interviewers or differences among those areas allocated to the interviewers (area effects), or both. Furthermore, the conventional wisdom in survey research suggests that it is advisable to have the same interviewers return to the same respondents in order to maintain good response rates in longitudinal surveys, though once again there has been very little documented experimental research to support this. This paper makes use of the interpenetrated sample design experiment in Wave 2 of the British Household Panel Study (BHPS) (i) to explore the effects of interviewers' background characteristics and years of experience on response rates, (ii) to identify and estimate the differential effects of interviewers on response rates and compare the magnitudes of area and interviewer effects, and (iii) to investigate the impact of interviewer continuity. The analysis is facilitated by the use of cross-classified multilevel modelling. The paper also looks at the issue of interviewer continuity qualitatively, through the impressions of the interviewers themselves.     

Structuring Corporate Headquarters: An Investigation of Franchising

This article focuses on the structuring of the corporate headquarters in a franchise organization. Four essential issues that are related to franchisors organizational structure are discussed—homogeneity and heterogeneity of franchisors structure, company-owned and franchise arrangement, the dynamics between strategy and structure, and performing innovative and administrative functions simultaneously in the headquarters. Propositions are given for each issue. The results of qualitative analysis associated with each issue are discussed.     

Wrapped distributions and measurement errors

Summary For a random variableX and >0 letU n (X)–X, wheren (x)=nZ iffx(n–/2,n+/2]. Random variables of this type are important in the theory of measurement errors. We derive formulas for the distribution ofU and apply them to the case XN(,²). General conditions for the unimodality ofU are given. The correlation of the measurement errorsX–E (X) andU (X) is seen to beO (^j) withj depending on the smoothness and asymptotic behavior of the density ofX. This gives a precise sense to the assertion that scale errors upwards and downwards are averagely well-balanced. In the normal case the density ofU is shown to be constant up to , as 0.     

Some brief notes on the “unfinished business” of qualitative inquiry

The paper argues that there are a variety of implicit issues in qualitative inquiry that need to be addressed if the area is to develop in some normal science sense. This unfinished business is concerned with a deeper investigation of basic terms that are now simply taken for granted, such as theme and pattern. It also includes the need to develop rules which will assist in making and justifying how qualitative interpretations are made from the implicit processes of inference. Specific suggestions are made for accomplishing these issues.     

Optimality of block designs with variable block sizes and random block effects

We consider the simple block model with random block effects, the block effects having variance _b ² =²;, with ² the variance of the errors. It is assumed that the experimenter can vary the sizes of the blocks. The universal optimality of certain designs for all over all designs with the same number of blocks and the same number of observations is shown. It is of interest to note that if Balanced Incomplete Block Designs compete, then they perform equally well for =0 and for =, i.e. in the one way classification model and in the simple block model with fixed block effects, but they perform worse for every (0, ).The result is, however, theoretical in nature. It treats a situation which is not very likely to happen in practice. The interest lies in the fact that it provides a counterexample to a conjecture on optimality of designs in mixed models.     

Cost-Output Relation,Technological Progress,and Clinical Activity Mix of US Hospital Pharmacies

The fairly recent discovery and growing use of costly, revolutionary biotechnology drugs (e.g., GM-CSFs) in hospitals represent a major technical innovation in clinical pharmacy intervention. This paper models the translog production cost impacts of ten distinct clinical pharmacy tasks including pharmacokinetics, consultations with MDs, monitoring drug interactions,..., and presents results on decomposed technical change, economies of scope, scale economies, total factor productivity, and the alternatively defined pairwise factor substitution possibilities. The model was fitted to 1981–1990 time-series/cross-sectional data of US hospital pharmacies (source: Eli-Lilly Co.®). Zellner's ISURE (Iterative Seemingly Unrelated Regression Equations) system estimates reveal a non-homothetic underlying technology with biased and pure technical change effects dominating scale-augmentation. Certain clinical tasks increase costs but are cost-saving if jointly produced with selective others. One of the largest and statistically significant economies of scope estimates is between monitoring drug interactions and consultations with MDs. Cost implications of findings are given in light of the recent trends in hospital pharmacy clinical activities, related professional health manpower, and piecemeal health policy reforms.     

Cascaded channels and the equivocation inequality

The variation of the equivocation and the average mutual information over cascaded channels is studied, using the generalized information measures (entropies of degree ) and Renyi information measures (entropies of order ). The equivocation inequality, which indicates that the equivocation can never decrease as we go further from the input on a sequence of cascaded channels, is shown to be satisfied by Renyi entropies (for 0<<1) for all channels and all probability distributions. The generalized entropies are shown to satisfy this inequality for binary symmetric channels for certain probability distributions The relations among the mutual information measures between the different terminals of the sequence of cascaded channels are studied, considering both the generalized and Renyi entropies. A necessary and sufficient condition for transmitting information without any loss across cascaded channels is obtained, when Renyi entropies are applied. The same condition is proved to be sufficient for achieving the equivocation equality (which indicates the case of no information loss across cascaded channels) over the class of binary symmetric channels, when the generalized entropies are applied.     

Das maximale signifikanzniveau des Tests: “LehneH o ab,wennk untern gegebenen tests zur ablehnung führen”

Summary On one sample space there aren tests with critical regionsK ₁ and levels of significance _i ,i=1, ...,n (resp.n eventsK _i in a probability space with probabilities not greater than _i ,i=1, ...,n). In this paper we calculate the smallest upper bound of the level of significance of the test reject the hypothesis, if at leastk among the,n tests do so (resp. of the probability of the event at leastk among then events are realized). By the way, we will show, that this smallest upper bound does not change, if we replace at leastk by exactlyk.     

The transition from central planning to a market economy: A computable general equilibrium model

This paper develops a computable general equilibrium (CGE) model of the transition from a central planned economy to a market economy. The model is an extension of Wellisz and Findlay's (1986) model of the Soviet second economy. By distinguishing alternative assumptions about the disposition of the government budget, two model variants — the activist and non-activist — are analyzed. Equilibria of these model variants are computed for various parameter specifications of the Kantorovich ray, which represents the stringency of central planners' direction of the economy. The paper shows that increasing efficiency of the private sector, while it reduces the size of government subsidies to the state sector, does not necessarily increase the net government budget.     

On the power of nonparametric changepoint-tests

We consider a sequenceX _1n,..., X_nn, n N, of independent random elements. Suppose there exists a [0, 1) such thatX _1n,...,X _(n),n have the distribution v₁ andX _[n]+1.n ,...,X _nn have the distribution v₂v₁. We construct consistent level- tests forH ₀:=0 versusH ₁:(0, 1), which are based on certainU-statistic type processes. A detailed investigation of the power function is also provided.     

Sulla dipendenza continua della probabilità di rovina dal caricamento dei premi

Si studia un modo di approssimare la probabilità di rovina relativa a un caricamento ₀ con le probabilità di rovina relative a una successione di caricamenti ( _k ) _k , che approssimano ₀ quandok tende all'infinito.

---

Summary In this paper we study a way of approximating the probability of ruin related to a loading ₀, by the probabilities of ruin related of a sequence of loadings ( _k ) _k which «approximate» ₀ ask converges to infinity.

     

The large-sample power of the 195-1195-1195-1test for multidimensional contingency tables

Summary The asymptotic power of the frequency ² test depends on a noncentrality parameter, ,Mitra [1958] offered a general expression for , which is rather difficult to apply. This work provides simplified formulae for in various models associated with multidimensional contingency tables.     

A two-stage stratified Warner’s randomized response model using optimal allocation

This paper applies Kim and Wardes (2004) stratified Warners randomized response model to Mangat and Singhs (1990) two-stage randomized response model. The proposed stratified randomized response model has an optimal allocation and a large gain in precision. Hence, the estimator based on the proposed method is more efficient than Kim and Wardes (2004) and Mangat and Singhs (1990) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.     

Two-dimensional Bernstein polynomial density estimators

A Bernstein polynomial estimator for f_nN(x, y) for an unknown probability density functionf(x, y) concentrated on the triangle ={(x, y): 0x, y<1,x+y<1} or on the square =(x, y):0 x, y 1 is developed. As a measure of quality the exact order of magnitude for the pointwise mean squared error is established. It is seen that the quality of these Bernstein polynomial estimators is comparable with the quality of the so-called kernel estimators. Further for such estimators uniform weak consistency results and central limit theorems are developed.     

Über die Anzahl von Zufallspunkten mit typ-gleichem nächsten Nachbarn und einen multivariaten Zwei-Stichproben-Test

Summary For independents-variate samplesX ₁, ...,X _m i.i.d.f. (.),Y ₁, ...,Y _n i.i.d. g. (.), where the densitiesf (.),g (.) are assumed to be continuous on their respective sets of positivity, consider the numberT _m,n of pointsZ of the pooled sample (which are either of typeX or of typeY) such that the nearest neighbor ofZ is of the same type asZ. We show that, as , independently of (.). An omnibus test for the two sample problem f(.)g(.) orf(.)g(.)? may be obtained by rejecting the hypothesisf(.)g(.) for large values ofT _m,n.     

Vergleich des verallgemeinerten nichtzentralent-Tests mit dem Binomialtest

Zusammenfassung Es sei {F _,(x); –<<, >0} mitF _,(x)=F((x–)/)–F(x) eine standardisierte Verteilungsfunktion — die Familie der zulässigen Verteilungsfunktionen. Der (früher eingeführte) verallgemeinerte nichtzentralet-Test für die Hypothese {PP ₀} mitP:=F _,(x ₀) gegen die Alternative {P>P ₀} zum Niveau wird mit dem entsprechenden nichtparametrischen Test (Test für die Hypothese {pP ₀} über den Parameterp einer Binomialverteilung gegen die Alternative {p>P ₀}) verglichen. Für dent-Test wird die relative asymptotische Effizienz bestimmt.Beide Tests lassen sich als Tests für das zur WahrscheinlichkeitP ₀ gehörende Quantil einer Verteilungsfunktion interpretieren. Der klassische zentrale Student-Test ergibt sich als Spezialfall (F(x)=(x),P ₀=0,5).

---

Summary Let {F _,(x);–<<, >0} withF _,(x ₀):=F((x–)/–F(x) a standarized distribution function — the family of admissible distribution functions. The (earlier introduced) generalized noncentralt-test for the hypothesis {PP ₀} withP:=F _,(x ₀) against the alternative {P>P ₀} at level of significance is compared with the corresponding nonparametric test (Binomial test). The relative asymptotic efficiency of thet-test is determined. Both kinds of tests can be interpreted as quantiltests. In caseF(x)=(x),P ₀=0,5 one gets the classical central Student-test.

     

Charakterisierung der zweiseitigen Exponentialverteilung

LetF () be a family of distribution functions with a translation parameter such thatF (0) has a densityf. It is well known that each sample median is a maximum likelihood estimate of , iff belongs to the classE of all bilateral exponential densities which are symmetric about 0. Here it is shown that, conversely,fE holds, either if there is an evenm such that for every sample of sizem each median is an MLE of , or if there is an infinite setM such that for every sample of any sizemM at least one median is an MLE of .