estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

a nonparametric multidimensional latent class irt model in a bayesian framework we propose a nonparametric item response theory model for dichotomously scored items in a bayesian framework the model is based on a latent class lc formulation and it is multidimensional with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class moreover an innovative system of prior distributions is proposed following the encompassing approach in which the largest model is the unconstrained lc model a reversible jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model by suitably post processing its output we then make inference on the number of dimensions i e number of groups of items measuring the same latent trait and we cluster items according to the dimensions when unidimensionality is violated the approach is illustrated by two examples on simulated data and two applications based on educational and quality of life data

the mathematical structure of rainfall representations 3 some applications of the point process theory to rainfall processes part 3 constitutes the final part of three parts devoted to the mathematical structure of rainfall the objective is to illustrate the scope of the tools developed in part 2 in the mathematical description of rainfall and rainfall driven processes a general overview of the three part series is given in part 1

model selection for multivariate regression in small samples we develop a small sample criterion aicc for selecting multivariate regression models this criterion adjusts the akaike information criterion to be an exact unbiased estimator for the expected kullback leibler information a small sample comparison shows that aicc provides better model order choices than other available model selection methods data from an agricultural experiment are analyzed

conditional distributions of neyman scott models for storm arrivals and their use in irrigation scheduling count for the widely recognized but often neglected statistical dependence in storm arrivals gabriel and newmann 1957 1962 smith and schreiber 1973 kavvas and delleur 1975 recently authors like kavvas and delleur 1975 and gupta and waymire 1979 have argued that this dependence is due to clustering of rainfall in time and space they suggest modeling storm arrivals with cluster point processes like the neyman scott model this work uses the concept of cluster models for storm arrivals the conditional distribution of the occurrence of future events given a history of the timing of past events is derived for the neyman scott model this new result is then used with a reformulated model of the irrigation scheduling problem now the decision of when and how much to irrigate is based on the time since the last observed storm the effective soil moisture content and the amount of available irrigation water a case study is presented to illustrate the solution significantly there is no important difference between the theoretical net benefits derived from assuming a homogeneous independent poisson model or a dependent neyman scott n s model during the growing season a nonhomogeneous poisson model yields higher theoretical benefits as expected the conditional n s model leads to improved irrigation control as compared to the unconditional n s model from this case study however no definite conclusion can be drawn regarding whether the neyman scott model better represents the process of storm arrivals as opposed to the poisson model however the expected opportunity loss of choosing the wrong model can be significant interesting implications of the results are that data manipulation can have a significant effect on the ultimate model

asymptotically efficient selection of the order by the criterion autoregressive transfer function on montre que la propriete d optimalite obtenue par shibata 1980 1981 est valable pour l approche cat parzen 1974 cat parzen 1977 et cat 2 bhansali 1985

euler class group of a laurent polynomial ring local case abstract let r be a noetherian commutative ring of dimension n 2 and let a r t t 1 assume that the height of the jacobson radical of r is at least 2 let p be a projective a module of rank n dim a 1 with trivial determinant we define an abelian group called the euler class group of a denoted by e a let be an isomorphism from a to det p to the pair p we associate an element of e a called the euler class of p denoted by e p then we prove that a necessary and sufficient condition for p to have a unimodular element is the vanishing of e p in e a earlier bhatwadekar and raja sridharan have defined the euler class group of r denoted by e r and have proved similar results for projective r module of rank n later m k das defined the euler class group of the polynomial ring r t denoted by e r t and proved similar results for projective r t modules of rank n with trivial determinant

compatibility of continuous rainfall occurrence models with discrete rainfall observations inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made following the work of i rodriguez iturbe et al 1984 this assertion is tested by examining the compatibility of the neyman scott n s model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day the results suggest that the n s model is inconsistent at different time scales and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought these findings are quite general in that they apply to any model with rainfall deposited instantaneously at times described by a n s process regardless of how the amounts associated with the events are distributed and of the dependence structure of the amounts

jackknife bias correction of the aic for selecting variables in canonical correlation analysis under model misspecification abstract in this paper we deal with a bias correction of akaike s information criterion aic for selecting variables in the canonical correlation analysis when a goodness of fit of the model is assessed by the risk function consisting of the expected kullback leibler loss function with a normal assumption although the bias of the aic to the risk function is o n 1 when the model is correctly specified its order turns into o 1 when the model is misspecified where n is the sample size by using the leave two out jackknife method with a constant adjustment we propose a new criterion that reduces the aic s bias to o n 2 even when the model is misspecified and is an exact unbiased estimator of the risk function when data is generated from the normal distribution additionally by applying basic theorems of linear algebra e g the formula of an inverse of the sum of matrices and a simple property of an inverse matrix to our problem we obtain strict conditions to guarantee the validity of the bias correction and another expression of the proposed criterion to reduce computational time tremendously which does not contain any jackknife estimators

finite sample criteria for autoregressive order selection the quality of selected ar models depends on the true process in the finite sample practice on the number of observations on the estimation algorithm and on the order selection criterion samples are considered to be finite if the maximum candidate model order for selection is greater than n 10 where n denotes the number of observations finite sample formulae give empirical approximations for the statistical average of the residual energy and of the squared error of prediction for several autoregressive estimation algorithms this leads to finite sample criteria for order selection that depend on the estimation method the special finite sample information criterion fsic and combined information criterion cic are necessary because of the increase of the variance of the residual energy for higher model orders that has not been accounted for in other criteria only the expectation of the logarithm of the residual energy as a function of the model order has been the basis for the previous classes of asymptotical and finite sample criteria however the behavior of the variance causes an undesirable tendency to select very high model orders without the special precautions of fsic or cic

a new method for the real time operation of reservoir systems this paper introduces a new method for the real time operation of reservoir systems the system is represented by a set of stochastic differential equations describing the reservoir and river dynamics in state space form the formulated reservoir operation problem calls for finding policies which maximize the expected benefits of one system s objective while satisfying the remaining objectives at prespecified reliability levels the solution is obtained by a new method named extended linear quadratic gaussian elqg controller elqg draws on and extends stochastic control theory results and it is well suited for the optimization of constrained dynamical systems it is a trajectory iteration algorithm theoretically expected to exhibit reliability and computational efficiency the new method is tested and evaluated in a real world case study

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

some properties of projective modules over discrete hodge algebras all rings in this paper are assumed to be commutative with 1 and all modules finitely generated let b be a discrete hodge algebra over a r ing a by definition this means that b r i where r a xi x and i is an ideal in r generated by monomials t vorst showed in 1 12 that thebehavior of projective modules over such b is very similar to the case of an ordinary polynomial ring in the following sense if all projective modules over any polynomial ring with ground ring a are extended from a then every projective module over a discrete hodge algebra over a is extended from a let b be a discrete hodge algebra over a noetherian ring a and p a projective module over b s mandal proved in 7 that if rank p dim b dim a 1 then

stability results for projective modules over blowup rings let r be a normal affine domain of dimension n 3 over an algebraically closed field k suppose chark 0 or chark p n let g f1 fr be a r regular sequence and a r f1 g fr g let p be a stably free a module of rank n 1 then murthy proved that there exists a projective r module q such that q r a p and n 1 q r 9 theorem 2 10 as a consequence of murthy s result if f g c x1 xn with g 0 then all stably free modules over c x1 xn f g of rank n 1 are free 9 corollary 2 11 in this paper we prove the following result 3 5 which generalizes the above result of murthy

model averaging by jackknife criterion in models with dependent data abstract the past decade witnessed a literature on model averaging by frequentist methods for the most part the asymptotic optimality of various existing frequentist model averaging estimators has been established under i i d errors recently hansen and racine hansen b e racine j 2012 jackknife model averaging journal of econometrics 167 38 46 developed a jackknife model averaging jma estimator which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors in this paper we broaden hansen and racine s scope of analysis to encompass models with i a non diagonal error covariance structure and ii lagged dependent variables thus allowing for dependent data we show that under these set ups the jma estimator is asymptotically optimal by a criterion equivalent to that used by hansen and racine a monte carlo study demonstrates the finite sample performance of the jma estimator in a variety of model settings

irrigation control in the presence of salinity extended linear quadratic approach an intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic elq control the elq control is well suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon a conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration for the intraseasonal model to be effective against perennial salt accumulation in the root zone it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season thus avoiding any significant leaching prior to the next growing season this long term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level the elq control is employed in a case study of expected net benefit maximization over an irrigation season of corn in fort morgan colorado the results in general correspond well with expected irrigation schedules under different conditions and provide valuable information on both short and long term aspects of irrigation control under saline conditions the elq control being an analytic iterative solution scheme with theoretically guaranteed fast convergence has a distinct computational advantage over state of the art procedures

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

exploring the model space and ranking a best class of models in surface wave dispersion inversion application at european strong motion sites abstractthe inversion of surface wave dispersion curve to derive shear wave velocity profile is a very delicate process dealing with a nonunique problem which is strongly dependent on the model space parameterization when independent and reliable information is not available the selection of most representative models within the ensemble produced by the inversion is often difficult we implemented a strategy in the inversion of dispersion curves able to investigate the influence of the parameterization of the model space and to select a best class of models we analyzed surface wave dispersion curves measured at 14 european strong motion sites within the neries ec project we focused on the inversion task exploring the model space by means of four distinct parameterization classes composed of layers progressively added over a half space the classes differ in the definition of the shear wave velocity profile we considered models with uniform velocity as well as models with increasing velocity with d

intraseasonal water allocation in deficit irrigation this paper is concerned with the optimal temporal allocation of irrigation water taking into consideration the intraseasonal stochastic variation of the crop water requirements and the dynamics of the soil moisture depletion process expressions for the soil moisture transition probabilities over a given time period and the first two moments of associated actual evapotranspiration are derived analytically the conditional probabilities of soil moisture and associated actual evapotranspiration are used within a stochastic dynamic programing dp algorithm with rewards being a function of cost and crop yield the dp algorithm is used to determine optimal control policies at each irrigation decision point conditional on the state of the system soil moisture content both mean and variance of net benefits are computed analytic results are corroborated with a case study example

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

properties and estimation of asymmetric exponential power distribution the new distribution class asymmetric exponential power distribution aepd proposed in this paper generalizes the class of skewed exponential power distributions sepd in a way that in addition to skewness introduces different decay rates of density in the left and right tails our parametrization provides an interpretable role for each parameter we derive moments and moment based measures skewness kurtosis expected shortfall it is demonstrated that a maximum entropy property holds for the aepd distributions we establish consistency asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix where the results apply to the sepd class they enlarge on the current literature also we give a convenient stochastic representation of the distribution our monte carlo study illustrates the theoretical results we also provide some empirical evidence for the usefulness of employing aepd errors in garch type models for predicting downside market risk of financial assets

the mathematical structure of rainfall representations 2 a review of the theory of point processes part 2 constitutes the second of three parts devoted to the mathematical structure of rainfall an expository yet current treatment of those features of point process theory which are essential to descriptions of the hydrologic processes is developed a general overview of this three part series is given in part 1

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

the mathematical structure of rainfall representations 1 a review of the stochastic rainfall models this is the first of a three part series on the mathematical structure of rainfall models several important attempts at modeling rainfall are reviewed special attention is given to the mathematical structures that arise in the rainfall descriptions a general overview of the three part series is given as preface to this part

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

bias corrected aic for selecting variables in multinomial logistic regression models abstract in this paper we consider the bias correction of akaike s information criterion aic for selecting variables in multinomial logistic regression models for simplifying a formula of the bias corrected aic we calculate the bias of the aic to a risk function through the expectations of partial derivatives of the negative log likelihood function as a result we can express the bias correction term of the bias corrected aic with only three matrices consisting of the second third and fourth derivatives of the negative log likelihood function by conducting numerical studies we verify that the proposed bias corrected aic performs better than the crude aic

the serre problem for discrete hodge algebras all rings in this paper will be commutative and noetherian let a b be a split injection of rings a finitely generated projective b module is called extended from a if there exists a finitely generated projective a module q such that p q b furthermore we call an c eglr b resp slr b extended from a if can be written as f i with fi glr a resp slr a and 7 e b the group of elementary matrices now let a be a ring in this paper we will consider a algebras of the following type a x1 xn i where i is an ideal generated by monomials such an a algebra is called a discrete hodge algebra over a and vice versa every discrete hodge algebra over a is of this type 5 for the proofs of most of our results we can restrict ourselves to the special class of square free discrete hodge algebras over a by which is meant that i can be generated by square free monomials the varieties over a corresponding to these square flee discrete hodge algebras are unions of intersections of coordinate hyperplanes h i x 1 xn anixi 0 i 1 n typical examples are a x 1 xn and a x 1 x 2 x i x 2 the main result of this paper is the following

projective modules over overrings of polynomial rings abstract let a be a commutative noetherian ring of dimension d and let p be a projective r a x 1 x l y 1 y m 1 f 1 f m module of rank r max 2 dim a 1 where f i a y i then i the natural map r gl r r el r 1 r k 1 r is surjective 3 8 ii assume f i is a monic polynomial then r 1 is an isomorphism 3 8 iii el 1 r p acts transitively on um r p in particular p is cancellative 3 12 iv if a is an affine algebra over a field then p has a unimodular element 3 13 in the case of laurent polynomial ring i e f i y i i ii are due to suslin 1977 12 iii is due to lindel 1995 4 and iv is due to bhatwadekar lindel and rao 1985 2

the euler class group of a polynomial algebra with coefficients in a line bundle let a be a commutative noetherian ring and p be a projective a module of rank text dim a 1 an intriguing open question is to find the precise obstruction for p to split as p simeq q oplus a for some a module q in this paper we settle this question when a r t for some ring r containing the field of rationals and p is a projective a module of rank text dim r

a stochastic cluster model of daily rainfall sequences a two level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension the model is a cluster process of the neyman scott type the model has the rainfall generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level it uses infinite superposition of rainfalls and has a very flexible dependence structure the model is fitted to daily rainfall sequences in indiana after these are stationarized by a transformation the fit of the model is then tested in terms of its correlation and marginal probability characteristics the present form of the neyman scott cluster model is time homogeneous therefore the neyman scott process as presented in this paper may be of practical use only for modeling the stationary rainfall occurrences

is there an optimal forecast combination abstract we consider several geometric approaches for combining forecasts in large samples a simple eigenvector approach a mean corrected eigenvector and trimmed eigenvector approach we give conditions where geometric approach yields identical result as the regression approach we also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination monte carlos are conducted to compare the finite sample performance of these and some popular forecast combination and information combination methods and to shed light on the issues of forecast combination vs information combination we also try to shed light on whether there exists an optimal forecast combination method by comparing various forecast combination methods to predict us real output growth rate and excess equity premium

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

variable selection with incomplete covariate data summary application of classical model selection methods such as akaike s information criterion aic becomes problematic when observations are missing in this article we propose some variations on the aic which are applicable to missing covariate problems the method is directly based on the expectation maximization em algorithm and is readily available for em based estimation methods without much additional computational efforts the missing data aic criteria are formally derived and shown to work in a simulation study and by application to data on diabetic retinopathy

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

on automorphisms of modules over polynomial rings write f xfi bxf then f is in xp and f q 0 clearly 1 qf is in el p x and it is a lift of 1 pg in a similar way we can lift 1 pg when g is unimodular this completes the proof of 2 8 the following is a variant of a proposition of lindel l 2 71 see 4 3 for the statement like the proposition of lindel in his paper this proposi tion plays a key roll in the proof of our main theorems 3 1 and 3 2 we shall go into detailed discussions on lindel s proposition l 2 71 in our later sections sects 4 5 6 and now we shall state our proposition 2 9

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

on the existence of unimodular elements and cancellation of projective modules over noetherian and non noetherian rings let r be a commutative ring of dimension d s r x or r x 1 x and p a finitely generated projective s module of rank r then p is cancellative if p has a unimodular element and r d 1 moreover if r dim s then p has a unimodular element and therefore p is cancellative as an application we prove that if r is a ring of dimension d of finite type over a prufer domain and p is a projective r x or r x 1 x module of rank at least d 1 then p has a unimodular element and is cancellative

modified aic and cp in multivariate linear regression the akaike information criterion aic and the mallows c p criterion have been proposed as approximately unbiased estimators for their risks or underlying criterion functions in this paper we propose modified aic and c p for selecting multivariate linear regression models our modified aic and modified c p are intended to reduce bias in situations where the collection of candidate models includes both underspecified and overspecified models in a simulation study it is verified that the modified aic and modified c p provide better approximations to their risk functions and better model selection than aic and c p

the euler class group of a polynomial algebra in this paper we continue our study on the theory of the euler class group of a polynomial algebra a t where a is a commutative noetherian ring containing q of dimension n for such a ring a in 9 we defined the notion of the nth euler class group en a t of a t for simplicity let us call it e a t in 9 we also studied the relations between e a t and e a where e a is the nth euler class group of a for example there is canonical map e a e a t which is an injective group homomorphism and it is an isomorphism when a is a smooth affine domain 9 proposition 5 7 in general these two groups are not isomorphic see discussion preceding 9 proposition 5 7 in this context the following question is natural