spectral properties of the transition operator associated to a multivariate refinement equation given a finitely supported sequence a on z s and an s s dilation matrix m the transition operator ta is the linear operator defined by tavoau a p b2z s aomabuvobu where a2 z s and v lies in 0oz s u the linear space of all finitely supported sequences on z s in this paper we investigate the spectral properties of the transition operator ta and apply these properties to the study of the approximation and smoothness properties of the normalized solution of the refinement equation a p a2z s aoau omau 1999

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

convergence of nonstationary cascade algorithms a nonstationary multiresolution of l 2 mathbb r s is generated by a sequence of scaling functions phi k in l 2 mathbb r s k in mathbb z we consider phi k that is the solution of the nonstationary refinement equations phi k m sum j h k 1 j phi k 1 m cdot j k in mathbb z where h k is finitely supported for each k and m is a dilation matrix we study various forms of convergence in l 2 mathbb r s of the corresponding nonstationary cascade algorithm phi k n m sum j h k 1 j phi k 1 n 1 m cdot j as k or n tends to infty it is assumed that there is a stationary refinement equation at infty with filter sequence h and that sum k h k j h j infty the results show that the convergence of the nonstationary cascade algorithm is determined by the spectral properties of the transition operator associated with h

the wishart autoregressive process of multivariate stochastic volatility abstract the wishart autoregressive war process is a dynamic model for time series of multivariate stochastic volatility the war naturally accommodates the positivity and symmetry of volatility matrices and provides closed form non linear forecasts the estimation of the war is straighforward as it relies on standard methods such as the method of moments and maximum likelihood for illustration the war is applied to a sequence of intraday realized volatility covolatility matrices from the toronto stock market tsx

convergence of multidimensional cascade algorithm a necessary and sufficient condition on the spectrum of the restricted transition operator is given for the convergence in l 2 bbb r d of the multidimensional cascade algorithm for any starting function phi 0 whose shifts form a partition of unity

pedestrian detection via classification on riemannian manifolds we present a new algorithm to detect pedestrian in still images utilizing covariance matrices as object descriptors since the descriptors do not form a vector space well known machine learning techniques are not well suited to learn the classifiers the space of d dimensional nonsingular covariance matrices can be represented as a connected riemannian manifold the main contribution of the paper is a novel approach for classifying points lying on a connected riemannian manifold using the geometry of the space the algorithm is tested on inria and daimlerchrysler pedestrian datasets where superior detection rates are observed over the previous approaches

a kernel two sample test we propose a framework for analyzing and comparing distributions which we use to construct statistical tests to determine if two samples are drawn from different distributions our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel hilbert space rkhs and is called the maximum mean discrepancy mmd we present two distribution free tests based on large deviation bounds for the mmd and a third test based on the asymptotic distribution of this statistic the mmd can be computed in quadratic time although efficient linear time approximations are available our statistic is an instance of an integral probability metric and various classical metrics on distributions are obtained when alternative function classes are used in place of an rkhs we apply our two sample tests to a variety of problems including attribute matching for databases using the hungarian marriage method where they perform strongly excellent performance is also obtained when comparing distributions over graphs for which these are the first such tests

the maximal smoothing principle in density estimation abstract we propose a widely applicable method for choosing the smoothing parameters for nonparametric density estimators it has come to be realized in recent years e g see hall and marron 1987 scott and terrell 1987 that cross validation methods for finding reasonable smoothing parameters from raw data are of very limited practical value their sampling variability is simply too large the alternative discussed here the maximal smoothing principle suggests that we consider using the most smoothing that is consistent with the estimated scale of our data this greatly generalizes and exploits a phenomenon noted in terrell and scott 1985 that measures of scale tend to place upper bounds on the smoothing parameters that minimize asymptotic mean integrated squared error of density estimates such as histograms and frequency polygons the method avoids the extreme sampling variability of cross validation by using ordinary scale estimators such as the standard deviation and interquartile range which

characterization of smoothness of multivariate refinable functions in sobolev spaces wavelets are generated from refinable functions by using multiresolution anlalysis in this paper we investigate the srloothness properties of multivariate refinable functionis in sobolev spaces we characterize the optinlal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant subspace several examples are provided to illustrate the general theory

convergence of cascade algorithms in sobolev spaces and integrals of wavelets the cascade algorithm with mask a and dilation m generates a sequence phi n n 1 2 ldots by the iterative process

using the refinement equation for evaluating integrals of wavelets the wavelet galerkin method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets this paper studies the problem from the point of view of stationary subdivision schemes one of the main results is to identify these integrals as components of the unique solution of a certain eigenvector moment problem associated with the coefficients of the refinement equation asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach

econometric analysis of realized covariation high frequency based covariance regression and correlation in financial economics this paper analyses multivariate high frequency financial data using realized covariation we provide a new asymptotic distribution theory for standard methods such as regression correlation analysis and covariance it will be based on a fixed interval of time e g a day or week allowing the number of high frequency returns during this period to go to infinity our analysis allows us to study how high frequency correlations regressions and covariances change through time in particular we provide confidence intervals for each of these quantities

convergence of cascade algorithms in sobolev spaces associated with multivariate refinement equations abstract this paper is concerned with multivariate inhomogeneous refinement equations written in the form x z s a mx g x x r s where is the unknown function defined on the s dimentional euclidean space r s g is a given compactly supported function on r s a is a finitely supported sequence on z s and m is an s s dilation matrix with m det m let 0 be an initial function in the sobolev space wk2 r s for n 1 2 define n x z s a n 1 mx g x x r s in this paper we give a characterization for the strong convergence in the sobolev space wk2 r s k n of the cascade sequence n n n for the case in which m is isotropic

construction of smooth refinable function vectors by cascade algorithms this paper establishes an equivalent relation between the convergence of a cascade algorithm in sobolev space and the convergence of an associated cascade algorithm in lp space it reduces the convergence in sobolev space to that in lp space on the other hand by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in sobolev space it is very easy to implement the algorithm examples are given to illustrate the theory

portfolio optimization with ambiguous correlation and stochastic volatilities in a continuous time economy we investigate the asset allocation problem among a risk free asset and two risky assets with an ambiguous correlation between the two risky assets the portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst case scenario with respect to the possible choice of correlation thus it becomes a maximin problem we solve the problem under the black scholes model for risky assets with an ambiguous correlation using the theory of g brownian motions we then extend the problem to stochastic volatility models for risky assets with an ambiguous correlation between risky asset returns an asymptotic closed form solution is derived for a general class of utility functions including constant relative risk aversion and constant absolute risk aversion utilities when stochastic volatilities are fast mean reverting we propose a practical trading strategy that combines information from the option implied volatilit

stability implies convergence of cascade algorithms in sobolev space this article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in sobolev space to which the refinable function vector belongs an example of hermite interpolants is presented to illustrate the result

mean variance portfolio selection with correlation risk the markowitz mean variance portfolio selection mvps problem is the building block of modern portfolio theory since markowitz 1952 published his seminal study there have been numerous extensions to the continuous time mvps problem under different market conditions this paper further enriches the literature by taking account of correlation risk among risky asset returns empirical studies reveal that correlations among economic variables change randomly over time and affect hedging and investment demand in different correlation regimes by incorporating correlation risk into the dynamic mvps through the wishart variance covariance matrix process this paper derives the explicit closed form solution to the optimal portfolio policy and determines the market regime in which the optimal policy is stable and well behaved this stable market regime is found to be fully characterized by the correlation between market returns and their variance covariance matrix or equivalently the effects of market leverage

mean variance approximations to expected utility abstract it is often asserted that the application of mean variance analysis assumes normal gaussian return distributions or quadratic utility functions this common mistake confuses sufficient versus necessary conditions for the applicability of modern portfolio theory if one believes as does the author that choice should be guided by the expected utility maxim then the necessary and sufficient condition for the practical use of mean variance analysis is that a careful choice from a mean variance efficient frontier will approximately maximize expected utility for a wide variety of concave risk averse utility functions this paper reviews a half century of research on mean variance approximations to expected utility the many studies in this field have been generally supportive of mean variance analysis subject to certain initially unanticipated caveats

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

mean variance portfolio selection with random parameters in a complete market this paper concerns the continuous time mean variance portfolio selection problem in a complete market with random interest rate appreciation rates and volatility coef cients the problem is tackled using the results of stochastic linear quadratic lq optimal control and backward stochastic differential equations bsdes two theories that have been extensively studied and developed in recent years specifically the mean variance problem is formulated as a linearly constrained stochastic lq control problem solvability of this lq problem is reduced in turn to proving global solvability of a stochastic riccati equation the proof of existence and uniqueness of this riccati equation which is a fully nonlinear and singular bsde with random coefficients is interesting in its own right and relies heavily on the structural properties of the equation efficient investment strategies as well as the mean variance efficient frontier are then analytically derived in terms of the solution of this equation in particular it is demonstrated that the efficient frontier in the mean standard deviation diagram is still a straight line or equivalently risk free investment is still possible even when the interest rate is random finally a version of the mutual fund theorem is presented

the shape and term structure of the index option smirk why multifactor stochastic volatility models work so well state of the art stochastic volatility models generate a volatility smirk that explains why out of the money index puts have high prices relative to the black scholes benchmark these models also adequately explain how the volatility smirk moves up and down in response to changes in risk however the data indicate that the slope and the level of the smirk fluctuate largely independently although single factor stochastic volatility models can capture the slope of the smirk they cannot explain such largely independent fluctuations in its level and slope over time we propose to model these movements using a two factor stochastic volatility model because the factors have distinct correlations with market returns and because the weights of the factors vary over time the model generates stochastic correlation between volatility and stock returns besides providing more flexible modeling of the time variation in the smirk the model also provides more flexible modeling of the volatility term structure our empirical results indicate that the model improves on the benchmark heston stochastic volatility model by 24 in sample and 23 out of sample the better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension

dynamic cointegrated pairs trading cointegration is a useful econometric tool for identifying assets which share a common equilibrium cointegrated pairs trading is a trading strategy which attempts to take a profit when cointegrated assets depart from their equilibrium this paper investigates the optimal dynamic trading of cointegrated assets using the classical mean variance portfolio selection criterion to ensure rational economic decisions the optimal strategy is obtained over the set of time consistent policies from which the optimization problem is enforced to obey the dynamic programming principle we solve the optimal dynamic trading strategy in a closed form explicit solution from a nonlinear hamilton jacobi bellman partial differential equation this analytical tractability enables us to prove rigorously that cointegration ensures the existence of statistical arbitrage using a dynamic time consistent mean variance strategy via asymptotic analysis this provides the theoretical grounds for the market belief in cointegrated pairs trading comparison between time consistent and precommitment trading strategies for cointegrated assets shows the former to be a persistent approach whereas the latter makes it possible to generate infinite leverage once a cointegrating factor of the assets has a high mean reversion rate

eigenvalues of spl darr 2 h and convergence of the cascade algorithm this paper is about the eigenvalues and eigenvectors of spl darr 2 h the ordinary fir filter h is a convolution with a vector h h o h n which is the impulse response the operator spl darr 2 downsamples the output y h x keeping the even numbered components y 2n where h is represented by a constant diagonal matrix this is a toeplitz matrix with h k on its kth diagonal the odd numbered rows are removed in spl darr 2 h the result is a double shift between rows yielding a block toeplitz matrix with 1 spl times 2 blocks iteration of the filter is governed by the eigenvalues if the transfer function h z spl sigma h k z sup k has a zero of order p at z 1 corresponding to spl omega spl pi then spl darr 2 h has p special eigenvalues 1 2 1 4 1 2 sup p we show how each additional zero at spl pi divides all eigenvalues by 2 and creates a new eigenvector for spl lambda 1 2 this eigenvector solves the dilation equation spl phi t 2 spl sigma h k spl phi 2t k at the integers t n the left eigenvectors show how 1 t t sup p 1 can be produced as combinations of spl phi t k the dilation equation is solved by the cascade algorithm which is an infinite iteration of m spl darr 2 2h convergence in l sup 2 is governed by the eigenvalues of t spl darr 2 2hh sup t corresponding to the response 2h z h z sup 1 we find a simple proof of the necessary and sufficient condition for convergence

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification

quadratic hedging and mean variance portfolio selection with random parameters in an incomplete market this paper concerns the problems ofquadratic hedging andpricing andmean variance portfolio selection in anincomplete market setting with continuous trading multiple assets and brownian information in particular we assume throughout that the parameters describing the market model may be random processes we approach these problems from the perspective oflinear quadratic lq optimal control and backward stochastic differential equations bsdes that is we focus on the so calledstochastic riccati equation sre associated with the problem excepting certain special cases solvability of the sre remains an open question our primary theoretical contribution is a proof of existence and uniqueness of solutions of the sre associated with the quadratic hedging and mean variance problems in addition we derive closed form expressions for the optimal portfolios and efficient frontier in terms of the solution of the sre a generalization of themutual fund theorem is also obtained

on the influence of the kernel on the consistency of support vector machines in this article we study the generalization abilities of several classifiers of support vector machine svm type using a certain class of kernels that we call universal it is shown that the soft margin algorithms with universal kernels are consistent for a large class of classification problems including some kind of noisy tasks provided that the regularization parameter is chosen well in particular we derive a simple sufficient condition for this parameter in the case of gaussian rbf kernels on the one hand our considerations are based on an investigation of an approximation property the so called universality of the used kernels that ensures that all continuous functions can be approximated by certain kernel expressions this approximation property also gives a new insight into the role of kernels in these and other algorithms on the other hand the results are achieved by a precise study of the underlying optimization problems of the classifiers furthermore we show consistency for the maximal margin classifier as well as for the soft margin svm s in the presence of large margins in this case it turns out that also constant regularization parameters ensure consistency for the soft margin svm s finally we prove that even for simple noise free classification problems svm s with polynomial kernels can behave arbitrarily badly

currency option pricing with wishart process it has been well documented that foreign exchange rates exhibit both mean reversion and stochastic volatility in addition to these recent empirical evidence shows a stochastic skew of implied volatility surface from currency option data which means that the slope of implied volatility curve of a given maturity is stochastically time varying this paper develops a currency option pricing model which accommodates for this phenomena the proposed model postulates that the log currency value follows a mean reverting process with stochastic volatility driven by wishart process under risk neutral measure pricing formula for european currency option is derived in terms of fourier transform benchmarking against the monte carlo simulation our numerical examples reveal that the pricing formula is accurate and remarkably efficient the proposed model is also generalized to include jumps the ability of the our model on capturing stochastic skew is illustrated through a numerical example

approximation properties of multivariate wavelets wavelets are generated from refinable functions by using multiresolution analysis in this paper we investigate the approximation properties of multivariate refinable functions we give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask we connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators finally we demonstrate that a refinable function in w k 1 1 r s provides approximation order k

distribution matching embedding for visual domain adaptation domain invariant representations are key to addressing the domain shift problem where the training and test examples follow different distributions existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space this space however may not be directly suitable for such a comparison since some of the features may have been distorted by the domain shift or may be domain specific in this paper we introduce a distribution matching embedding approach an unsupervised domain adaptation method that overcomes this issue by mapping the data to a latent space where the distance between the empirical distributions of the source and target examples is minimized in other words we seek to extract the information that is invariant across the source and target data in particular we study two different distances to compare the source and target distributions the maximum mean discrepancy and the hellinger distance furthermore we show that our approach allows us to learn either a linear embedding or a nonlinear one we demonstrate the benefits of our approach on the tasks of visual object recognition text categorization and wifi localization