IN T R O D U C T IO N
T h e set o f p apers we w ould like to present is the result o f th e 17th In te rn a tio n a l C onference on M u ltiv a riate S tatistical A nalysis o rganized by In stitu te o f S tatistical M eth o d s, U niversity o f L o dz an d P olish S tatistical A ssociation. T h e conference was held in the period 30 N ov em b er - 1 D e cem ber 1998 in Lodz. I he scope o f subjects discussed d u rin g th e co n feren ce was very wide - Irom the latest theoretical achievem ents in m a th e m a tical statistics to th eir application s in various disciplines: finance, in surance and risk th eo ry . T h e m a jo r stress has alw ays been p u t o n statistica l m eth ods.
T h e selected papers have been grouped in to th ree th em atic sections: 1. S tatistical M ethods.
2. S tatistical Inference.
3. A p p licatio n o f Statistical M eth o d s.
I he first p ap e r devoted to the problem s o f statistical m odels, entitled C lassification into I wo P o p u latio n s for Tim e D e p end ent O b se rv a tio n s” was proposed by M irosław K rzy śk o and W ald em ar W ołyński. T h e a u th o rs studied the optim al classification rules based o n linear fu n ctio n s which m axim ize area u n d er the relative o p eratin g ch aracteristic curve o r which m axim ize the chosen p robabilistic distance betw een tw o p o p u latio n s. It h as been show n th a t the resulting p rocedure belongs to the A n d e rso n -B a h a d u r adm issible class and the expression for the optim al linear d iscrim inate fu n ctio n has been presented.
B ronisław C era n k a and K ry sty n a K a tu lsk a in th eir p ap e r “ A nalysis o f V ariance w ith lim e Series D a ta ” considered the lik elih o o d -ratio crite ria testing the hypothesis oi equality o f the g ro u p m eans, un der th e assu m p tio n th a t th ere is a ra n d o m effect fo r each in d iv id u al an d th e successive o b serv atio n s o n each individual follow A R m odel.
T h e next p ap e r by K ry sty n a P ru sk a entitled “ B o o tstra p D istrib u tio n o f O L S -E stim ato rs fo r L inear R egression M o d els” focused on th e results o f sim ulation experim ents fo r linear m odels w ith erro rs w hich have n o rm al, stu d en t o r uniform distrib u tio n .
A ndrzej G rzybow ski in the p ap e r “ O n U n c ertain ty C lasses and M inim ax E stim atio n in the L inear R egression M odels w ith Ilctero sccd asticity and C o rre la ted E rro rs” proposed tw o m odels o f the u n certain ty know ledge (the so called uncertain ty classes). T h e first one m ay represent the problem o f estim atio n for heterosccdastic m odel, the o th er m ay reflect th e u n certain ty connected with the presence o f correlation am ong errors. M inim ax estim ators were o b tain ed and som e num erical exam ples were discussed as well.
T h e last p ap e r in this section: “ E v alu a tio n o f th e P ro bab ility C o n te n t as an Infinite L inear C o m b in atio n o f W ishart D istrib u tio n s” by H elena Jclcnkow ska was concerned with the problem o f getting unified estim ato rs as the conditio n al po sterio r m eans o f m ultiv ariate inverted m atrics o f D irichled distrib u tio n .
G rzeg orz M alinow ski in the p ap e r “ Logical M any-V aluedness V ersus P ro b a b ility ” presents an d discusses th e m o st d irec t issues on re la tio n betw een logical m any - valuedness and logical probability i.e. th e prob ab ility related to proposition.
T h e next section entitled “ Statistical Inference” starts with the co ntrib ution o f Jan u sz W ywiał: “ E stim atio n o f M ode on the Basis o f a T ru n c a te d S am ple” . T h e a u th o r presents the problem o f estim ation o f the m o d e o f a co n tin u o u s d istrib u tio n function. M oreover, the accuracy o f th e m o d e estim atio n is studied on the basis o f co m p u ter sim ulation.
G rażyna T rzpiot in the paper “M ultivalued Stop-Loss Stochastic D o m in an ce T e st” discussed the problem o f procedures used to identify the class o f decision alternatives in the case o f m ultivalued p ro b a b ility d istrib u tio n s.
T h e next paper entitled “ Sam ple B reakdow n P oints o f th e W ilcoxon and Sign T ests for L o c a tio n ” by Jerzy K orzeniew ski was concerned w ith the num erical values o f the b reak d o w n points o f the W ilcoxon and sign tests for location for the n o rm al d istrib u tio n .
T h e next section was devoted to the “ A pplication o f Statistical M e th o d s” and it consists o f six p apers concerning different econom ic an d biological problem s.
T h e first pap er “ O n U nem ploym ent Investigation in Small A re a s” by C zeslaw D o m ań sk i and K ry sty n a P ru sk a presents the m eth o d s o f sm all area statistics which can be applied to investigate the p h en o m en o n o f unem ploym ent in a given subpopulation depending on sam pling and additional in fo rm atio n a b o u t the p o p u latio n .
Czeslaw D om ański and Jarosław K o n d ra siu k in the paper “ Im p lem entin g o f A nalytic H ierarchy Process in B anking” used A H P m eth o d s to assign d ep o sit and b an k interest rates.
Z ofia H anusz in the p aper “ R elative Potency for the M ultivariable C o n ta m in ated N orm al R esponses” considered the im pact o f the resp on ses from co n tam in ated n o rm al d istrib u tio n on the relative potency.
I he p ap e r “ M odel o f C onnection Between In fla tio n and In terest R ate Based on the Polish F inan cial M a rk e t” by Stefania G in alsk a an d B eata S k o w ro n -G rab o w sk a focused on som e em pirical m odels o f financial m ark e ts based on F ran k el exchange rates.
Iw o n a N o w akow ska in the presen tatio n “T h e P ro d u ctio n A nalysis by D ual D ynam ic P ro g ra m m in g ” considered the concept o f du ality th eo ry for dynam ic production process with constraints i.e. p rod uction process described by nonconvex dynam ic m ath em atical m odels.
T h e paper entitled “ O n the A verage R etu rn R ate for a G ro u p o f Investm ent b u n d s ” by Lesław G ajek and M arek K a łu sz k a was concerned with the definition o f the average return rate which is derived via in tegration ol the financial results o f the g rou p o f funds d u rin g a given period o f tim e.
Czesław D om ański Alina Jędrzejczak
