on quick attribute reduction in decision theoretic rough set models compared with the pawlak rough set model decision theoretic rough set dtrs models have relatively powerful data processing capability for complex and low quality data however the non monotonicity of the criteria used in dtrs models causes many problems particularly the inefficiency of attribute reduction algorithms which greatly narrows their applications few systematic studies have been reported on how to construct efficient reduction methods for dtrs models this paper discusses this problem and constructs an efficient reduction algorithm for dtrs models incorporating three aspects taking advantage of common characteristics of data sets and employing division techniques a fast division approach to computing equivalence classes is proposed which is the most frequently used and the most time consuming basic operation in the reduction algorithm extracting a monotonic ingredient from decision systems an effective heuristic function is constructed for the reduction algorithm which can guide searches for the algorithm and has better ability to find shorter super reducts a novel algorithm is proposed to search the power set space of a given super reduct which has a shorter average search length than the existing backtracking methods finally the reduction algorithm is proposed that combines these improvements experimental results demonstrate that these improvements are effective and the proposed reduction algorithm is relatively efficient

approximations of marginal tail probabilities and inference for scalar parameters summary in many situations inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density for such inference accurate approximations of marginal tail probabilities are useful to avoid high dimensional integrals two tail probability approximations are developed in this paper numerical results given for conditional inference in location scale and linear regression models show the approximations to be generally accurate even for small sample sizes

normal families new perspectives this paper surveys some surprising applications of a lemma characterizing normal families of meromorphic functions on plane domains these include short and efficient proofs of generalizations of i the picard theorems ii gol dberg s theorem a meromorphic function on c which is the solution of a first order algebraic differential equation has finite order and iii the fatou julia theorem the julia set of a rational function of degree d 2 is the closure of the repelling periodic points we also discuss bloch s principle and provide simple solutions to some problems of hayman connected with this principle over twenty years ago on the way to a partial explication of the phenomenon known as bloch s principle i proved a little lemma characterizing normal families of holomorphic and meromorphic functions on plane domains 68 over the years the lemma has grown and in dextrous hands proved amazingly versatile with applications to a wide variety of topics in function theory and related areas with the renewed interest in normal families arising largely from the important role they play in complex dynamics it seems sensible to survey some of the most striking of these applications to the one variable theory with the aim of making this technique available to as broad an audience as possible that is the purpose of this report one pleasant aspect of the theory is that judicious application of the lemma often leads to proofs which seem almost magical in their brevity in such cases we have made no effort to resist the temptation to write out complete proofs hardly anything beyond a basic knowledge of function theory is required to understand what follows so the reader is urged to take courage and plough on through and now we turn to our tale 1 let d be a domain in the complex plane c we shall be concerned with analytic maps i e meromorphic functions f d r2 received by the editors october 15 1997 and in revised form may 26 1998 1991 mathematics subject classification primary 30d45 secondary 30d35 34a20 58f23

reducts and constructs in classic and dominance based rough sets approach abstract the idea of the reduct as defined in the classic rough sets approach crsa has proven to be inspiring enough to get into closely related theories including the dominance based rough sets approach drsa the procedure of reduction is generally similar to that of feature selection but narrower as it is the descriptive rather than the predictive aspect of data exploration that constitutes its principal goal crsa reducts are thus defined as minimal subsets of attributes that retain sufficiently high quality of object description developed within crsa the crsa reducts have given rise to the generalized notion of crsa constructs which have turned out to be superior to reducts in numerous practical experiments with real life data sets the generalization process is continued in this paper in which a definition of constructs in the context of drsa is introduced the definition fully analogous to that of crsa constructs differs only in that it is context based in drsa while context free in crsa consequently the presented drsa constructs are expected to have analogous properties to that of crsa constructs including superiority to drsa reducts in experiments with real life data sets

class specific feature sets in classification in this correspondence we present a new approach to the design of probabilistic classifiers that circumvents the dimensionality problem rather than working with a common high dimensional feature set the classifier is written in terms of likelihood ratios with respect to a common class using sufficient statistics chosen specifically for each class

normal families of meromorphic functions concerning shared values abstract in this paper we study the problem of normal families of meromorphic functions concerning shared values and prove that a family f of meromorphic functions in a domain d is normal if for each pair of functions f and g in f f a f n and g a g n share a value b in d where n is a positive integer and a b are two finite constants such that n 4 and a 0 this result is not true when n 3

the relationship between attribute reducts in rough sets and minimal vertex covers of graphs the problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both np hard problems this paper studies the relationship between the two problems the vertex cover problem for graphs from the perspective of rough sets is first investigated the attribute reduction of an information system is then studied in the framework of graph theory the results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph conversely the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph finally a new algorithm for the vertex cover problem based on rough sets is presented furthermore experiments are conducted to verify the effectiveness of the proposed method

prediction and tolerance intervals with transformation and or weighting we consider estimation of quantiles and construction of prediction and tolerance intervals for a new response following a possibly nonlinear regression fit with transformation and or weighting we consider the case of normally distributed errors and to a lesser extent the nonparametric case in which the error distribution is unknown quantile estimation here follows standard theory although we introduce a simple computational device for likelihood ratio testing and confidence intervals prediction and tolerance intervals are somewhat more difficult to obtain we show that the effect of estimating parameters when constructing tolerance intervals can be expected to be greater than the effect in the prediction problem improved prediction and tolerance intervals are constructed based on resampling techniques in the tolerance interval case a simple analytical correction is introduced we apply these methods to the prediction of automobile stopping distances and salmon production using respectively a he

on the relation between rough set reducts and typical testors this paper studies the relations between rough set reducts and typical testors from the so called logical combinatorial approach to pattern recognition definitions comments and observations are formally introduced and supported by illustrative examples furthermore some theorems expressing theoretical relations between reducts and typical testors are enunciated and proved we also discuss several practical applications of these relations that can mutually enrich the development of research and applications in both areas although we focus on the relation between the classical concepts of testor and reduct our study can be expanded to include other types of testors and reducts

measures of the sensitivity of regression estimates to the choice of estimator abstract let y 1 y n denote independent real valued observations each of the form y j x j e j where x j is a fixed covariate vector and are unknown parameters e1 e n are identically distributed according to a symmetric density p this article considers the sensitivity of point estimates of to the choice of estimator from classes of estimators based on the l estimators of kroenker and portnoy specific measures of sensitivity are proposed these measures are applied to several datasets

quick attribute reduction in inconsistent decision tables this paper focuses on three types of attribute reducts in inconsistent decision tables assignment reduct distribution reduct and maximum distribution reduct it is quite inconvenient to judge these three types of reduct directly according to their definitions this paper proposes judgment theorems for the assignment reduct the distribution reduct and the maximum distribution reduct which are expected to greatly simplify the judging of these three types of reducts on this basis we derive three new types of attribute significance measures and construct the q ara quick assignment reduction algorithm the q dra quick distribution reduction algorithm and the q mdra quick maximum distribution reduction algorithm these three algorithms correspond to the three types of reducts we conduct a series of comparative experiments with twelve uci machine learning data repository university of california at irvine data sets including consistent and inconsistent decision tables to evaluate the performance of the three reduction algorithms proposed with the relevant algorithm quickreduct 9 34 the experimental results show that quickreduct possesses weak robustness because it cannot find the reduct even for consistent data sets whereas our proposed three algorithms show strong robustness because they can find the reduct for each data set in addition we compare the q dra quick distribution reduction algorithm with the cebarknc conditional entropy based algorithm for reduction of knowledge without a computing core 43 because both find the distribution reduct by using a heuristic search the experimental results demonstrate that q dra runs faster than cebarknc does because the distribution function of q dra has a lower calculation cost instructive conclusions for these reduction algorithms are drawn from the perspective of classification performance for the c4 5 and rbf svm classifiers last we make a comparison between discernibility matrix based methods and our algorithms the experimental results indicate that our algorithms are efficient and feasible

relative reducts in consistent and inconsistent decision tables of the pawlak rough set model a relative reduct can be considered as a minimum set of attributes that preserves a certain classification property this paper investigates three different classification properties and suggests three distinct definitions accordingly in the pawlak rough set model while the three definitions yield the same set of relative reducts in consistent decision tables they may result in different sets in inconsistent tables relative reduct construction can be carried out based on a discernibility matrix the study explicitly stresses a fact that the definition of a discernibility matrix should be tied to a certain property regarding the three classification properties we can define three distinct definitions accordingly based on the common structure of the specific definitions of relative reducts and discernibility matrices general definitions of relative reducts and discernibility matrices are suggested

min max attribute object bireducts on unifying models of reducts in rough set theory abstract a decision table describes a finite set of objects ob by using a finite set of condition attributes c and a finite set of decision attributes d pawlak defines attribute reducts by considering the entire decision table as a generalization we introduce the notion of min max attribute object bireducts of a sub table restricted by a pair b x of a subset of condition attributes b and a subset of objects x a pair r z is a min max attribute object bireduct of b x if and only if r is a minimal subset of b such that r and b make the same correct decisions for objects in x and z is a maximal subset of x for which b can make the correct decisions we propose the notion of the decidability of objects and introduce the decidable region of a set of objects as a generalization of the positive region of the set we define and interpret a min max attribute object bireduct based on the decidable region min max attribute object bireducts offer a general model and existing models of attribute reducts are special cases the results lead to a unified framework for studying four types of attribute reducts

generation of rough sets reducts and constructs based on inter class and intra class information the reduct originating from the classic rough set approach crsa is an inclusion minimal subset of attributes that provides discernibility between objects from different classes in at least the same degree as the set of all attributes it can be thus referred to as being consistent and minimal which are the two important characteristics of filter based feature selection these two characteristics have been also utilized to define reducts within the dominance based rough set approach drsa further the classic reduct here referred to as an inter class reduct has evolved into what is known as intra class reduct and construct in crsa the idea is that while inter class reducts utilize only one part of information generated from all pairs of objects intra class reducts utilize the remaining part while constructs utilize both the paper delivers a final unification of inter class reducts intra class reducts and constructs across crsa and drsa showing how they can be both defined and computed uniformly i e using basically the same concepts and algorithms it also presents an exact algorithm capable of generating all exact reduced subsets but of considerable complexity as well as a simple and fast heuristic designed to generate a single reduced subset finally it illustrates the computation process with examples and some experimental evaluation of crsa constructs which show how the use of both the inter class and the intra class information can assist the attribute reduction process and help obtaining useful insights into the analyzed data set

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

comparisons of approximate confidence intervals for distributions used in life data analysis this article evaluates the accuracy of approximate confidence intervals for parameters and quantiles of the smallest extreme value and normal distributions the findings also apply to the weibull and the lognormal distributions the interval estimates are based on a the asymptotic normality of the maximum likelihood estimator b the asymptotic x 2 distribution of the likelihood ratio lr statistic c a mean and variance correction to the signed square roots of the lr statistic and d the bartlett correction to the lr statistic the extensive monte carlo results about true error probabilities and average lengths under various degrees of censoring show advantages of the lr based intervals for complete or moderately censored samples the mean and variance correction to the lr statistic gives nearly exact and symmetric error probabilities in small samples with heavy censoring the bartlett correction tends to give conservative error probabilities whereas the uncorrected lr interval is often antico

attribute reduction in decision theoretic rough set models rough set theory can be applied to rule induction there are two different types of classification rules positive and boundary rules leading to different decisions and consequences they can be distinguished not only from the syntax measures such as confidence coverage and generality but also the semantic measures such as decision monotocity cost and risk the classification rules can be evaluated locally for each individual rule or globally for a set of rules both the two types of classification rules can be generated from and interpreted by a decision theoretic model which is a probabilistic extension of the pawlak rough set model as an important concept of rough set theory an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table this paper addresses attribute reduction in decision theoretic rough set models regarding different classification properties such as decision monotocity confidence coverage generality and cost it is important to note that many of these properties can be truthfully reflected by a single measure c in the pawlak rough set model on the other hand they need to be considered separately in probabilistic models a straightforward extension of the c measure is unable to evaluate these properties this study provides a new insight into the problem of attribute reduction

an expanded double quantitative model regarding probabilities and grades and its hierarchical double quantitative attribute reduction a double quantitative model on probabilities and grades is proposed by integration the model with quantitative semantics expands dtrs model grs model pawlak model model regions are hierarchically and optimally calculated via two algorithms three reduct types srp reduct crp reduct app reduct are hierarchically studied the double quantitative reducts expand basic qualitative and quantitative reducts probabilities and grades serve as relative and absolute measures respectively they are used to establish the decision theoretic rough set dtrs and graded rough set grs two basic quantitative models the double quantification of probabilities and grades exhibits systematicness and completeness in view of the two dimensional feature of the approximate space however double quantitative construction becomes a problem and double quantitative reduction is rarely reported thus this paper mainly constructs an expanded double quantitative model by logically integrating probabilities and grades it further studies relevant double quantitative reduction by hierarchically preserving specific regions 1 first a novel model is established via the logic integration and expansion requirement and its regional system and granular hierarchy are studied via granular computing thus regional semantics is extracted via basic semantics granules regional calculation is realized by two algorithms and the algorithm regarding calculation granules exhibits optimization according to algorithm analyses 2 second three types of model regional preservation reducts and their hierarchy are discussed in the two category case thus srp reduct crp reduct and app reduct are studied by exploring four region preservation properties constructing two region classification regions and preserving four original approximations respectively furthermore a relevant reduction hierarchy is thoroughly achieved 3 moreover the model and its reduction are illustrated by two examples of decision tables the constructional model conducts double quantification regarding probabilities and grades thus it exhibits double quantitative semantics and benignly expands dtrs model grs model and pawlak model furthermore its hierarchical reduction reflects some double quantitative reduction essence thus its reduction expands qualitative pawlak reduction while guides quantitative dtrs reduction and grs reduction

finding rough and fuzzy rough set reducts with sat feature selection refers to the problem of selecting those input features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing in particular solution to this has found successful application in tasks that involve datasets containing huge numbers of features in the order of tens of thousands which would otherwise be impossible to process further recent examples include text processing and web content classification rough set theory has been used as such a dataset pre processor with much success but current methods are inadequate at finding globally minimal reductions the smallest sets of features possible this paper proposes a technique that considers this problem from a propositional satisfiability perspective in this framework globally minimal subsets can be located and verified

attribute reduction based on evidence theory in incomplete decision systems attribute reduction is a basic issue in knowledge representation and data mining this paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on dempster shafer theory of evidence the concepts of plausibility reduct and belief reduct in incomplete information systems as well as relative plausibility reduct and relative belief reduct in incomplete decision systems are introduced it is shown that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set in a consistent incomplete decision system the concepts of relative reduct relative plausibility reduct and relative belief reduct are all equivalent in an inconsistent incomplete decision system an attribute set is a relative plausibility reduct if and only if it is a relative reduct a plausibility consistent set must be a belief consistent set and a belief consistent set is not a plausibility consistent set in general

on normal families of meromorphic functions in this paper we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions which improve and generalize the related results of gu bergweiler and lin

data analysis based on discernibility and indiscernibility rough set theory models similarities and difierences of objects based on the notions of indiscernibility and discernibility with respect to any subset of attributes one can deflne two pairs of dual relations the strong indiscernibility and weak discernibility relations and the weak indiscernibility and strong discernibility relations the similarities of objects are examined by the indiscernibility relations and the difierence by the discernibility relations respectively alternatively one can construct an indiscernibility matrix to represent the family of strong indiscernibility or weak discernibility relations one also can construct a discernibility matrix to represent the family of strong discernibility or weak indiscernibility relations the consideration of the matrix counterpart of relations and the relation counterpart of matrices brings more insights into rough set theory based on indiscernibility and discernibility three difierent types of reducts can be constructed keeping the indiscernibility discernibility and indiscernibility anddiscernibility relations respectively although the indiscernibility reducts have been intensively studied in the literature the other two types of reducts are relatively new and require more attention the existing methods for constructing the indiscernibility reducts also can be applied to construct the other two types of reducts an empirical experiment for letter recognition is reported for demonstrating the usefulness of the discussed relations and reducts

a set covering based approach to find the reduct of variable precision rough set abstract attribute reduction is one of the core problems in rough set rs theory in the variable precision rough set vprs model attribute reduction faces two difficulties firstly in the vprs model a reduct anomaly problem may arise and it may cause an inconsistency of positive regions and decision rules after attribute reduction secondly the attribution reduction problem has been proved an np hard problem accordingly we would need to find a tradeoff between calculating the minimal reduct and reducing computing complexity to avoid the combinatorial explosion problem we propose a new approach to calculate the reduct in vprs model this new method focuses on calculating a distribution reduct while avoiding the anomaly problem in the vprs model the basic idea of the proposed approach is to convert the reduct problem into a set covering problem scp according to the positive regions in the vprs model and consequently a set covering heuristic function schf algorithm is applied to calculate the reduct after this conversion this approach keeps the positive regions consistent after the attribute reduction and moreover based on the scp the performance ratio of the proposed method to calculate the minimal reduct ranges between ln u ln ln u o 1 and 1 o 1 ln u with a computational complexity having an upper bound as o mn m n 2 finally we demonstrate the practical application of the vprs model using real case scenario from china s electricity power yield to verify the validity of our proposed approach we then apply statistical evaluation to explain the economic significance of the attributes

class specific attribute reducts in rough set theory abstract the concept of attribute reducts plays a fundamental role in rough set analysis there are at least two possibilities to define an attribute reduct a classification based or global attribute reduct is a minimal subset of condition attributes that preserves the positive region of the decision classification namely the positive regions of all decision classes in a decision table a class specific class dependent or local attribute reduct is a minimal subset of condition attributes that preserves the positive region of a particular decision class while a classification based reduct may not work equally well for every decision class a class specific attribute reduct is optimally tailored to a particular decision class however studies in rough set theory are dominated by classification based reducts there is very limited investigation on class specific reducts an objective of this paper is to draw attention to class specific reducts we systematically compare the two types of reducts and investigate their relationships with respect to both individual reducts and families of all reducts it is possible to derive a class specific reduct from a classification based reduct and to derive a classification based reduct from a family of class specific reducts the families of all class specific reducts provide a pair of lower and upper bounds of the family of all classification based reducts based on a three way classification of attributes into the pair wise disjoint sets of core marginal and nonuseful attributes we examine relationships between the corresponding classes of classification based and class specific attributes the union of the sets of class specific core attributes is the set of classification based core attributes it is only possible to obtain an upper bound for the set of classification based marginal attributes and a lower bound for the set of classification based nonuseful attributes from the family of the class specific corresponding sets of attributes

knowledge reduction based on the equivalence relations defined on attribute set and its power set one of the key problems of knowledge discovery is knowledge reduction this paper proposes a new method for knowledge reduction in information systems first two families of closed sets c r and c r are defined where r and r are equivalence relations defined on the attribute set and its power set respectively the properties of c r and c r are also discussed the necessary and sufficient condition for c r c r is then given and employed to construct an approach to attribute reduction in information systems it is also proved that under the condition c r c r the proposed approach to knowledge reduction is equivalent to the well accepted one in reference w x zhang y leung w z wu information systems and knowledge discovery science publishing company beijing 2003

decision region distribution preservation reduction in decision theoretic rough set model abstract in the pawlak rough set model the positive region the boundary region and the non negative region are monotonic with respect to the set inclusion of attributes however the monotonicity property of the decision regions positive region boundary region or non negative region with respect to the set inclusion of attributes does not hold in the decision theoretic rough set model therefore the decision regions may be changed after attribute reduction based on quantitative preservation or qualitative preservation of decision regions this effect is observed partly because three decision regions are defined by introducing the probabilistic threshold values in addition heuristic reduction algorithms based on decision regions may find super reducts because of the non monotonicity of decision regions to address the above issues this paper proposes solutions to the attribute reduction problem based on decision region preservation in the decision theoretic rough set model first the positive region distribution preservation reduct the boundary region distribution preservation reduct and the negative region distribution preservation reduct are introduced into the decision theoretic rough set model second three new monotonic measures are constructed by considering variants of the conditional information entropy from which we can obtain the heuristic reduction algorithms the results of the experimental analysis validate the monotonicity of new measures and verify the effectiveness of decision region distribution preservation reducts

local reduction of decision system with fuzzy rough sets one important and valuable topic in fuzzy rough sets is attribute reduction of decision system the existing attribute reductions with fuzzy rough sets consider all decision classes together and cannot identify key conditional attributes explicitly for special decision class in this paper we introduce the concept of local reduction with fuzzy rough sets for decision system the local reduction can identify key conditional attribute and offer a minimal description for every single decision class approach of discernibility matrix is employed to investigate the structure of local reduction at last several experiments are performed to show that the idea of local reduction is feasible and valid

a novel method for attribute reduction of covering decision systems attribute reduction has become an important step in pattern recognition and machine learning tasks covering rough sets as a generalization of classical rough sets have attracted wide attention in both theory and application this paper provides a novel method for attribute reduction based on covering rough sets we review the concepts of consistent and inconsistent covering decision systems and their reducts and we develop a judgment theorem and a discernibility matrix for each type of covering decision system furthermore we present some basic structural properties of attribute reduction with covering rough sets based on a discernibility matrix we develop a heuristic algorithm to find a subset of attributes that approximate a minimal reduct finally the experimental results for uci data sets show that the proposed reduction approach is an effective technique for addressing numerical and categorical data and is more efficient than the method presented in the paper d g chen c z wang q h hu a new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets information sciences 177 17 2007 3500 3518

hybrid attribute reduction based on a novel fuzzy rough model and information granulation feature subset selection has become an important challenge in areas of pattern recognition machine learning and data mining as different semantics are hidden in numerical and categorical features there are two strategies for selecting hybrid attributes discretizing numerical variables or numericalize categorical features in this paper we introduce a simple and efficient hybrid attribute reduction algorithm based on a generalized fuzzy rough model a theoretic framework of fuzzy rough model based on fuzzy relations is presented which underlies a foundation for algorithm construction we derive several attribute significance measures based on the proposed fuzzy rough model and construct a forward greedy algorithm for hybrid attribute reduction the experiments show that the technique of variable precision fuzzy inclusion in computing decision positive region can get the optimal classification performance number of the selected features is the least but accuracy is the best

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

three layer granular structures and three way informational measures of a decision table abstract attribute reduction in rough set theory serves as a fundamental topic for information processing and its basis is usually a decision table d table d table attribute reduction concerns three hierarchical types and only classification based reduction is related to information theoretic representation aiming at inducing comprehensive d table attribute reduction with hierarchies and information this paper concretely constructs a d table s three layer granular structures and three way informational measures via granular computing and bayes theorem with regard to the d table the micro bottom meso middle and macro top are hierarchically organized according to the formal structure and systematic granularity then different layers produce different three way informational measures by developing bayes theorem thus three way weighted entropies originate from three way probabilities at the micro bottom and further evolve from the meso middle to the macro top and their granulation monotonicity and evolution systematicness are acquired furthermore three way informational measures are analyzed by three layer granular structures to achieve their hierarchical evolution superiority and algorithms finally structural and informational results are effectively illustrated by a d table example this study establishes d table s hierarchical structures to reveal constructional mechanisms and systematic relationships of informational measures the obtained results underlie the d table s hierarchical systematic and informational attribute reduction and they also enrich the three way decisions theory

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

a second order investigation of asymptotic ancillarity the paper deals with approximate ancillarity as discussed by efron and hinkley 1978 in the multivariate i i d case we derive the second order edgeworth expansion of the mle given a normalized version of the second derivative of the log likelihood at its maximum the expansion agrees with the one derived by amari 1982a for curved exponential families but holds for any family satisfying the regularity conditions given in the paper it is shown that the fisher information lost by reducing the data to the mle is recovered by the conditioning and it is sketched how the loss of information relates to the deficiency as defined by lecam finally we investigate some properties of three test statistics proving a conjecture by efron and hinkley 1978 concerning the conditional null distribution of the likelihood ratio test statistic and establishing a kind of superiority of the observed fisher information over the expected one as estimate of the inverse variance of the mle

efficient attribute reduction from the viewpoint of discernibility attribute reduction is an important preprocessing step in pattern recognition machine learning and data mining as an effective method for attribute reduction rough set theory offers a useful and formal methodology it retains the discernibility power of the original datasets thus attribute reduction has been extensively studied in rough set theory however the inefficiency of the existing attribute reduction algorithms limits the application of rough sets in this paper we first analyse the limitations of existing attribute reduction algorithms then a novel measure of attribute quality called the relative discernibility degree is proposed based on the discernibility theoretical analysis shows that this measure can find relative dispensable attributes and remain unchanged after removing the relative dispensable attributes and redundant objects in the process of selecting attributes this property can be used to reduce the search space and accelerate the heuristic process of attribute reduction consequently a new attribute reduction algorithm is proposed from the viewpoint of discernibility furthermore the relationships among the reduction definitions of the algebra view information view and discernibility view are derived some non equivalent relationships among these views of rough set theory in inconsistent decision tables are discovered a set of numerical experiments was conducted on uci datasets experimental results show that the proposed algorithm is effective and efficient and is applicable to the case of large scale datasets

nullity based matroid of rough sets and its application to attribute reduction rough sets were proposed to deal with vagueness and incompleteness of knowledge in information systems in this field there are many optimization issues such as attribute reduction matroids generalized from matrices have been widely used in many fields particularly greedy algorithm design which plays an important role in attribute reduction therefore it is meaningful to combine matroids with rough sets to solve the optimization problems in this paper we construct a type of matroid of rough sets based on the concept of nullity and apply it to attribute reduction first we propose a nullity operator for rough sets to induce a matroid and then we present a specific type of matroid called a nullity based matroid second given the relationship between nullities and matrices we present two types of matrices to characterize this type of matroid and its nullity operator third the dual of this type of matroid is induced by the second type of matrix finally we apply the obtained matroids to attribute reduction issues in information systems in summary this paper provides a new approach to studying rough sets

practical small sample asymptotics for distributions used in life data analysis fraser and lawless discussed exact conditional intervals for the parameters and quantiles of the location scale model when complete data are used moreover lawless extended the exact method to failure censored type ii censored data nevertheless the exact intervals are difficult to obtain in practice and are unavailable under time censoring type i censoring as a consequence approximate large sample intervals are widely used in this article a likelihood based third order procedure is developed the method does not require explicit nuisance parameterization and can be easily implemented into algebraic computational packages numerical examples are presented to show the accuracy of the method even when the sample size is small

positive approximation an accelerator for attribute reduction in rough set theory feature selection is a challenging problem in areas such as pattern recognition machine learning and data mining considering a consistency measure introduced in rough set theory the problem of feature selection also called attribute reduction aims to retain the discriminatory power of original features many heuristic attribute reduction algorithms have been proposed however quite often these methods are computationally time consuming to overcome this shortcoming we introduce a theoretic framework based on rough set theory called positive approximation which can be used to accelerate a heuristic process of attribute reduction based on the proposed accelerator a general attribute reduction algorithm is designed through the use of the accelerator several representative heuristic attribute reduction algorithms in rough set theory have been enhanced note that each of the modified algorithms can choose the same attribute reduct as its original version and hence possesses the same classification accuracy experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

likelihood inference for linear regression models summary approximate conditional inference based on large sample likelihood ratio methods is considered for the parameters of linear regression models mean and variance adjustments that improve the standard normal approximation to the conditional distribution of the signed square root of the log likelihood ratio statistic for a scalar parameter of interest are given a bartlett adjustment factor that improves the chi squared approximation to the conditional distribution of the log likelihood ratio statistic for a vector parameter of interest is also presented the accuracy of approximate confidence limits obtained by using the adjustments is demonstrated for a location scale analysis of darwin s data

approximate inference for the generalized gamma distribution methods of approximate conditional inference in location and scale parameter distributions based on normal approximations to the distributions of signed square roots of likelihood ratio statistics are discussed these methods are applied to obtain approximate inference for the quantiles and scale parameter of the log generalized gamma distribution from uncensored samples assuming that the index parameter of the distribution is known as special cases approximate inference in the extreme value and normal distributions from type ii censored samples is considered the accuracy of the approximate methods for small samples is illustrated by comparison with exact results in some examples