IN T R O D U C TIO N
T h e a rtic le s we w ould like to p re sen t arc th e re su lts o f th e 21sl C onference on M u ltiv ariate Statistical A nalysis - M SA 2002. T h e conferen ce to o k place in Ł ódź, in the period 4 6 N ovem ber 2002. It was organised by th e U niversity o f Ł ó d ź (C h air o f S tatistical M e th o d s) and Polish Statistical A ssociation. T h e range o f subjects o f interests o f the C onference papers was wide, from the theory o f probability, th ro u g h statistical inferen ce to different applications o f statistical m eth o d s in various disciplines: finance, insurance and medicines.
T h e p ap ers arc divided into three them atic sections: 1. P robability.
2. Statistical Inference. 3. A pplications.
I he first p ap e r devoted to the use o f stochastic g rad ien t b oosting in n o n p aram etric tree-based regression was proposed by E ugeniusz G a tn a r (Gradient Boosting in Regression). T he au th o r studied th ree aggregation m eth o d s used in classification: b o o tstrap aggregation (bagging), adaptive resam ple and com bine (boosting) and adaptive bagging (hybrid bagging- boostin g procedure).
T ad eu sz G e rsten k o rn (A C om pound o f an In fla ted Pascal Distribution with the Poisson One) focused his atten tio n on a co m p o u n d o f an inflated Pascal distribution with the Poisson one. Probability function o f the com pound d istrib u tio n Pascal-Poisson, factorial, crude and incom plete m om ents as well recurrence relations o f this d istrib u tio n are presented.
T h e next p a p e r by K rz y szto f Jaju g a ( T ail D ependence in Bivariate Distributions) was concerned with the problem o f tail dependence for bivariate d a ta . T h e p a rtic u la r em phasis was p u t o n th e co n d itio n a l co rrelatio n coefficients and tail dependence coefficients. It was show n how the latter could be analyzed th ro u g h copula analysis.
G ra ży n a Irz p io t (Effectiveness o f Stochastic Dominance in Financial Analysis) focused on portfolio analysis th a t can be regarded as a problem o f choosing the best investm ent project from all possible investm ents. This choice depends on, the unique fo r each investor, utility fun ctio n and the distrib u tio n o f the re tu rn o f the investm ent project. T h e results o f analysis the properties o f the optim al efficient set according SD criteria fo r asym m etric d istrib u tio n w ere presented.
T h e p ap e r by Jerzy K orzeniew ski (Analysis o f Point Processes Observed with Noise with Applicational Example) presented an exam ple o f the application o f p o in t processes observed w ith noise arc aerial p h o to g ra p h s o f forests with the aim o f estim ating the actual nu m b er o f trees on a given area. A new algorithm to estim ate directly the num ber o f actual trees was proposed, w here th e only assum ptio n on which the new m easu re d epends is the n atu ral assu m p tio n ab o u t forest density being locally co n stan t.
Sebastian S itarz (Stochastic Orders in Discrete D ynam ic Programming) considered a p roblem o f dynam ic optim ization w ith values o f criteria fu nction in the set o f the random variables. D ynam ic m odel w ith finite nu m b er o f stages, states and decision variables was described. Such a dy nam ic process is evaluated regarding values o f the ran dom variables. T he ran d o m variables have to fulfil som e conditions, if they are to be applied to dynam ic o ptim ization. T hese conditions are described in presented paper and there is given a review o f stochastic orders, w hich can be used in the m odel.
T o m asz Jurkiew icz and K rzy szto f N ajm an (Proposition o f Applying К -M eans Classification M ethod and the S O M Type N eural N etw ork to Improve the E fficiency o f Sm all Domains E stim ation in a Representative S tu d y o f Sm a ll and M edium -Sized Enterprises) presented a p rop osition o f tw o -stag e estim atio n process. In the first stage, using th e S O M -type neural netw orks and using the к -m eans classification m eth o d the sim ilari ty o f co m p o n en ts belonging to the small d om ain w ith th e com ponents belonging to the rem aining p art of the sam ple is determ ined. T h e second step consists in using the inform ation only from those do m ain s, which are sim ilar to the studied small d om ain with the help o f approp riately construed weights. A u th o rs presented the results o f the above procedure in the analysis o f the building industry on the basis o f a representative study o f sm all and m edium -sized enterprises. T hey have also un dertak en an a tte m p t to estim ate the errors o f the synthetic estim atio n m ethod m odified in such a way.
In the p ap e r by T om asz Ż ądło {On Synthetic Ratio E stim ator Based on Superpopulation Approach), properties o f a prcdictor o f the form o f syn thetic ra tio estim ato r o f dom ain to tal, know n from ra n d o m isatio n ap p ro ach , were considered. T he p ro o f o f its ^-unbiasedness for sim ple regres sion su p erp o p u la tio n m odel in stra ta was show n. F o r the m odel BLU p red ictor was also presented. E quations o f prediction variances o f b oth predictors were derived. F o r considered predictors the problem o f m odel m isspecification was considered and equation s o f p redictio n m ean square errors were derived.
A dam D e p ta ( The Use o f Blume and Vasicek M ethods in the Estim ation o f Beta C oefficient in the Single-Index M odel) presented altern ativ e m ethods
o f valu atio n o f coefficients beta. T h e estim ation o f fu tu re coefficients beta can be received by delim itation the coefficients b eta from p ast d a ta and use these coefficients as the estim ation o f fu tu re coefficients beta.
T h e next section entitled Statistical Inference sta rts with the co n trib u tio n o f Czesław D om ań ski (Som e R em arks on Statistica l Inference fo r C om plex Samples). T h e a u th o r presented the problem s in estim ation and verifications o f hypothesis o f consistency o f d istribution s for com plex sam ples, where observatio ns in these sam ples are stochastically d epend ent and have different d istrib u tio n .
K ry sty n a P ru sk a (Tests fo r Ratio o f Two M eans in Case o f Sm all Areas) disscused testing procedures for verification o f hypothesis which says th at there is n o difference between the ra tio o f small area m ean and po p u latio n m ean for analysed variable and auxiliary variable. T h e pro perties o f one considered procedure were investigated with the use o f sim ulatio n m ethods.
T h e next p aper by Jan u sz W ywiał (On E stim ation o f Dominant o f M ultidim ensional Random Variable) considered the problem o f estim ation o f the m ode o f a continuous distribution function o f m ultidim ensional random variable. T he biased estim ators o f values o f m odal regressions were proposed. M oreover, the w ell-know n “jack k n ife” procedure was pro p o sed to evaluate the m ean sq uare erro rs o f the estim ators.
A lek sa n d ra B aszczyńska (Som e R em arks on the Choice o f the Kernel Function in Density Estimation) focused on kernel m ethod in density estimation, w ith p artic u la r em phasis on influence o f the choice o f the kernel function K (u ) on the q u an tity o f sm ooothing. M o n te C arlo study was presented, where seven kernel functions (G aussian, U niform , T riangle, E panechnikov, Q u artic, T riw eight, C osinus) are used in density estim ation.
W ojciech G a m ro t (On Application o f Logistic Regression to M ean Value E stim ation in Two-Phase Sam pling fo r Nonresponse) investigated alternative estim ators fo r tw o-phase sam pling scheme using estim ates o f response p robabilities obtained o n the basis o f logistic regression m odel. T he results o f M o n te C arlo sim ulation study com paring the properties o f these estim ators w ere also presented. In the sim ulations, the d a ta from the P olish 1996 A gricultural C ensus were used.
T h e next paper by A lina Jędrzejczak (Properties o f the C o x Consistency Test in the Case o f Income Distribution Analysis) presented m ain properties o f the C ox statistic which is based on likelihood ra tio . T h e presented results were o btained by m eans o f the M o n te C arlo experim ent. T h e theoretical d istrib u tio n s m o st often used in incom e d istrib u tio n analysis as the gam m a, lognorm al, D agum and S ingh-M addala were taken into consideration.
D o ro ta Pekasiew icz (Application o f Sim ulation M etho ds to Estim ation o f Variance o f Nonparam etric Sequential E stim ator o f M ean) proposed an applying sim ulation m ethods to estim ate the variance o f a n o n p aram etric
estim ato r o f m ean. A n application o f b o o tstra p m eth o d s to estim ate the variance o f a synthetic estim ato r o f the m ean in sequential estim atio n was also presented.
T h e last paper in this section by A gnieszka R o ssa ( Unbiased Estimation o f Survival Probabilities fo r Censored D ata with Known Censoring Times) investigated a class o f unbiased estim ators o f survival p ro b ab ility P ( T ,> t ) u nder random and independent censorship m odel is considered, where the p otential survival times T t are possibly unobserved, but the censoring times Z f and m in ( T t, Z () are know n and the sam ple size is ra n d o m .
In the g ro u p o f articles dealing with applications B ronislaw C eranka and M ałgorzata G raczyk (Construction o f O ptimum Balance Weighing Designs Based on Balanced Block Designs) discussed problem o f estim ation o f the individual u nknow n m easurem ents (weights) o f p objects w hen we have at o u r disposal n m easurem ent operations (weighings).
M ałg o rz ata M isztal (On the Application o f Classification and Regression Trees in M edical Diagnosis) considered a decision tree as a graphical presentation o f the recursive partitio ning the learning set into hom ogenous subsets considering dependent variable y. T h e aim o f this p ap e r is to present som e applications o f regression and classification trees in m edical diagnosis for solving decision - m ak ing problem s.
T he paper by A nna Szymańska (Application o f Selected Statistical M ethods in Assessing H om ogeneity o f Insurance Portfolio) focused on the assessm ent o f selected m eth o d s o f testing portfolio hom ogeneity illustrated with an exam ple o f m o to r insurance.
M o n ik a Zielińska (D ynam ic Schem es o f Hedging - D elta Hedging and D elta-G am m a Hedging on Currency M arket) presented tw o dynam ic schemes o f hedging: delta hedging and delta-gam m a hedging with exam ples from the P olish currency m arket. T he hedging techniques which reduce the loss w ithout excluding the profits from currency m ovem ents are given preference. T h eir application requires access to reliable forecasts o f fu tu re currency m ovem ents, as well as certain readiness to bear th a t kind o f risk.
I he p ap e r by Alicja G anczarek (A P T M o del For Electricity Prices on the D ay A head M a rket o f the Polish Power Exchange) considered m odel of the dependence o f the electricity price on m acroeconom ic factors such as changes in the d o llar price, the deutsche m ark price, the ra te o f inflation, the ra te o f unem ploym ent, price changes in th e m in in g ind u stry , the p ro d u c tio n o f the m anu factu rin g sector, the o u tp u t o f the m in ing industry and w eather conditions. T h e aim o f this article was th e em pirical verification o f the price m odel on the D ay A head M ark et (D A M ) o f the Polish Power Exchange in 2001 based on the principal com p on ents m ethod.
I om asz K o zd raj (R em arks on Bayesian N etw orks and Their Applications) focused on Bayesian netw orks th a t are directed acyclic g rap hs th a t represent
dependencies betw een variables in a probabilistic m odel. T h is p ap e r explores the n atu re o f im plications for Bayesian netw orks beginning with an overview and com parison o f inferential statistics and Bayes’ T heo rem . It presents the possibilities o f applications o f Bayesian netw orks in a field o f econom ic problem s and also focuses on the problem o f learning.
T h e next p aper by Jarosław M ichalak (Using C ontrol Charts to D etect Sm all Process Shifts) dealt with the selection o f p rop er SPC charts is essential to effective statistical process con tro l im plem entation and use. T his paper shows th a t, the C um ulative-sum control charts (C U S U M ) and E xponentially W eighted M oving Average control charts (E W M A ) arc a p p ro p riate to detect these shifts.
M arck Szajt (Identification o f P atent-A ctivity Level with the Usage o f Discriminant Analysis) tried to separate p articu lar co u n try groups in E urope on the basis o f p aten t activity. T h e division has been m ad e w ith the usage o f statistical m eth o d s - m ainly discrim inant function. T h e analysis presented in the thesis allows characterizing particu lar p artic ip a n ts and draw ing one’ s a tte n tio n to the differences in innovative policy co nd ucted in different countries.
T h e paper by A neta W łodarczyk, T om asz Szmigiel (Theoretical Aspects o f Using M a rko v M odels in Research o f Exchange R ate Volatility) was concerned with m odeling o f short-run exchange rate fluctuations using M arkov m odels.
Ja n Ż ółtow ski (Application o f Probit M odels and Selected Discrimination Analysis M eth ods fo r Credit Decision Evaluation) disscused th e problem o f evaluatio n to which o f the tw o groups the person applying for a credit should be assigned to: a) those who possess the creditw orthiness; b) those who do not possess the creditworthiness. It analyses the possibility o f applying the pro b it m odels and the discrim ination analysis m etho ds using the quadratic and linear discrim ination function. A n evaluation o f the correctness o f the classification based o n the real d a ta from a com m ercial ban k is conducted.
Aleksandra Baszczyńska Czeslaw D om ański
