This paper summarizes the parameter estimation of systems with set-valued signals, which can be classified to three catalogs:one-time completed algorithms, iterative methods and recursive algorithms. For one-time completed algorithms, empirical measure method is one of the earliest methods to estimate parameters by using set-valued signals, which has been applied to the adaptive tracking of periodic target signals. The iterative methods seek numerical solutions of the maximum likelihood estimation, which have been applied to both complex diseases diagnosis and radar target recognition. The recursive algorithms are constructed via stochastic approximation and stochastic gradient methods, which have been applied to adaptive tracking of non-periodic signals.
The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed. Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.
In this article, we consider the varying coefficient multiplicative regression model, which is very useful to model the positive response. The criterion of least product relative error (LPRE) is extended to the varying coefficient multiplicative regression model by kernel smoothing techniques. Consistency and asymptotic normality of the proposed estimator are established. Some numerical simulations are carried out to assess the performance of the proposed estimator. As an illustration, the ethanol data is analyzed.
For the hypersonic inlet and fore-body integrated design, the non-uniform incoming flow generated by the fore-body will bring a relatively big challenge to the inward-turning inlet design. To make the inlet match the non-uniform incoming flow, this paper, based on previous studies, develops a cross-stream marching plus (CSMP) method, by which an aerodynamic surface used to generate a given shock shape can be acquired. The method can correct such solution points as may give rise to grid distortions or flow-field abnormity and overcome the shortcoming of the insufficient stability of previous methods. Numerical simulation results of the conical supersonic flowfield show that the error obtained from the proposed CSMP method drops with the reduction of the grid dimension and the marching step, being less than 0.05% for reducing the marching step to 10%; that with this method the maximum relative error of the pressure on the profile is less than 0.23%. In the design process of the inward-turning inlets that match the fuselage fore-body, it's found that in comparison with the results of the inviscid CFD results, the aerodynamic surface designed with the CSMP method can fully generate the given shock wave shape. Thus, the CSMP method provides a new direction for the inlet/fore-body integrated design.
In this paper, we consider an improved model of pricing vulnerable options with credit risk. We assume that the vulnerable European options not only face default risk, but also face the rare shocks of the underlying assets and the counterparty assets. The dynamics of two correlated assets are modeled as a class of jump diffusion processes. Furthermore, we assume that the dynamic of the corporate liability is a geometric Brownian motion that is related to the underlying asset and the counterparty asset. Under this new framework, we give an explicit pricing formula of the vulnerable European options.
Gutman and Wagner (in the matching energy of a graph, Disc. Appl. Math., 2012) defined the matching energy of a graph and pointed out that its chemical applications go back to the 1970s. Now the research on matching energy mainly focuses on graphs with pendent vertices and only a few papers reported the progress on matching energy of graphs without pendent vertices. For a random six-membered ring spiro chain, the number of k-matchings and the matching energy are random variables. In this paper, we determine the extremal graphs with respect to the matching energy for random six-membered ring spiro chains which have no pendent vertices.
This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues. Compactness of the integral operator in L^{1}[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.
In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for characterization of multiscale limits for gradients and very weak multiscale convergence.
In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the[13] broad class of commutative search directions for cone of semidefinite matrices, extended by[18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.
In this paper, we investigate standing waves in discrete nonlinear Schrödinger equations with nonperiodic bounded potentials. By using the critical point theory and the spectral theory of self-adjoint operators, we prove the existence and infinitely many sign-changing solutions of the equation. The results on the exponential decay of standing waves are also provided.
In this paper, we use the Green's function method to get the pointwise convergence rate of the semilinear pseudo-parabolic equations. By using this precise pointwise structure and introducing negative index Sobolev space condition on the initial data, we release the critical index of the nonlinearity for blowing up. Our result shows that the global existence does not only depend on the nonlinearity but also the initial condition.
As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.
A dynamic actual demand function was used to portray a market environment for fast moving consumer goods and to establish oligopoly differential games under price competition. We confirmed the stable point in n-player price competition as the saddle point of differential games, and acquired the optimal price and demand at equilibrium. Analysis on optimal price and demand shows that, to obtain more profits, a manufacturer should control costs, rapidly occupy the market, and improve product uniqueness.
Censored regression ("Tobit") model is a special case of limited dependent variable regression model, and plays an important role in econometrics. Based on this model, all kinds of methods for variable or group variable selection have been developed and the corresponding shrinkage parameter estimates are widely studied. However, asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters, such as density function of error term. To avoid estimating nuisance parameters, this paper presents a randomly weighting method to approximate to the asymptotic distribution of the shrinkage estimate. A computation procedure of random approximation is provided and asymptotic properties of the randomly weighting estimates are also obtained. The proposed methods are evaluated with extensively numerical studies and a women labor supply example.
We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper. These problems arise in many applications of practical interest. A class of alternating linearization methods is presented for solving these problems. The global convergence rate is also obtained under certain mild conditions. Numerical experiments validate the theoretical convergence analysis and verify the implementation of the proposed algorithm.
A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-_{o-1}-heavy if every induced claw (K_{1,3}) of G has a pair of nonadjacent vertices with degree sum at least n - 1 in G. In this paper we show that a claw-_{o-1}-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.
For a graph G=(V, E) without isolated vertex, a function f:E(G) → {-1, 1} is said to be a signed star dominating function of G if ∑_{e∈E(v)}f(e) ≥ 1 for every v ∈ V (G), where E(v)={uv ∈ E(G)|u ∈ V (G)}. The minimum value of ∑_{e∈E(G)}f(e), taken over all signed star dominating functions f of G, is called the signed star domination number of G and is denoted by γ_{ss}(G). This paper studies the bounds and algorithms of signed star domination numbers in some classes of graphs. In particular, sharp bounds for the signed star domination number of a general graph and a linear-time algorithm for the signed star domination problem in a tree is presented.
Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical) if G - I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical, depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.
A non-increasing sequence π=(d_{1}, d_{2},…, d_{n}) of nonnegative integers is said to be potentially hamiltonian-graphic (resp. potentially pancyclic-graphic) if it is realizable by a simple graph on n vertices containing a hamiltonian cycle (resp. containing cycles of every length from 3 to n). A.R. Rao and S.B. Rao (J. Combin. Theory Ser.B, 13(1972), 185-191) and Kundu (Discrete Math., 6(1973), 367-376) presented a characterization of π=(d_{1}, d_{2},…, d_{n}) that is potentially hamiltonian-graphic. S.B. Rao (Lecture Notes in Math., No. 855, Springer Verlag, 1981, 417-440, Unsolved Problem 2) further posed the following problem:present a characterization of π=(d_{1}, d_{2},…, d_{n}) that is potentially pancyclic-graphic. In this paper, we first give solution to this problem for the case of 4 ≤ n ≤ 11. Moreover, we also show that a near regular graphic sequence π=(d_{1}, d_{2},…, d_{n}) with d_{n} ≥ 3 is potentially pancyclic-graphic.