the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

relative efficiency of estimates and the use of chebyshev polynomials in a model of pairwise overlapping samples abstract overlapping samples appear in several fields of statistical applications in a model of successive pairwise overlap we consider two parameter estimators for the expectation of underlying random variables the estimators are based on sample means having a tridiagonal covariance matrix we are interested in the behavior of the relative efficiency as a function of certain problem parameters representations in terms of chebyshev polynomials and some helpful relations lead to a monotonicity result which is then generalized to weighted sample means

some results on canonical correlation and their applications to a linear model abstract we show the monotonic properties of canonical correlation coefficients and the concave convex properties of some of their functions with respect to some elements of the variance covariance corresponding to them and then use these results to discuss the monotonic and concave convex properties of the relative efficiency of the least squares estimator lse in a linear regression model with respect to some elements of the variance covariance of the error vector finally we give two examples of the two stage sampling regression model and pairwise overlapping sampling regression model

spectral factorizations with unmixed pole and zero sets minimal spectral factors of spectral density matrices are constructed where poles and zeros lie in prescribed unmixed subsets of the complex plane

some comments on k tridiagonal matrices recently several papers emerged in the literature discussing the determinant the spectrum and the inverse of the so called k tridiagonal matrices the aim of this comment is to provide a general unified and attractive approach to them recalling some less known results

quantum and fisher information from the husimi and related distributions the two principal immediate influences which we seek to interrelate here upon the undertaking of this study are papers of yczkowski and slomczynski j phys a 34 6689 2001 and of petz and sudar j math phys 37 2262 1996 in the former work a metric the monge one specifically over generalized husimi distributions was employed to define a distance between two arbitrary density matrices in the petz sudar work completing a program of chentsov the quantum analog of the classically unique fisher information monotone metric of a probability simplex was extended to define an uncountable infinitude of riemannian also monotone metrics on the set of positive definite density matrices we pose here the questions of what is the specific unique fisher information metric for the classically defined husimi distributions and how does it relate to the infinitude of quantum metrics over the density matrices of petz and sudar we find a highly proximate small relative entropy relationship bet

a note on ordinary least squares methods for two stage sampling abstract a class of linear models for two stage sampling problems is considered ordinary least squares estimates are optimal for these models for some parameters the usual least squares estimates of standard errors are shown to be appropriate

bounds on the efficiency of estimates based on overlapping data summary if we have several estimates of the same quantity based on partially overlapping sets of data we can contemplate combining them linearly to give a single estimate we give bounds which depend only on the degrees of overlap but not on the individual variances for the efficiency of the best linear unbiased combination of these estimates with and without covariance information relative to the overall best linear unbiased estimate in particular if the sets have no more than pairwise overlap each of these partial information estimates has efficiency at least 8 9 this result holds also in the multivariate case and applies in an asymptotic sense when maximum likelihood estimates based on overlapping sets of data are combined linearly relative to the overall maximum likelihood estimate the result is applied to the problem of estimating a renewal distribution from time windowed realizations of several independent processes

inversion of a tridiagonal jacobi matrix abstract a formula for the inverse of a general tridiagonal matrix is given in terms of the principal minors

spectral factorization via hermitian pencils abstract the spectral factorization problem is solved for state space systems via results on the canonical forms and inertia of hermitian matrix pencils these algebraic results then give a deflation method for spectral factorization

inversion of tridiagonal matrices this paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist ukita s theorem is extended to characterize the class of matrices that have tridiagonal inverses

eigenproblems for tridiagonal 2 toeplitz matrices and quadratic polynomial mappings abstract given a system of monic orthogonal polynomials mops p n x n 0 we characterize all the sequences of monic orthogonal polynomials q n x n 0 such that q 1 x x b q 2 n x p n 2 x n 0 1 2 where 2 is a fixed polynomial of degree exactly 2 and b is a fixed complex number with an appropriate choice of the mops p n x n 0 our results enables us to solve the eigenproblem of a tridiagonal 2 toeplitz matrix giving an alternative proof to a recent result by m j c gover we also find the relations between the jacobi matrices corresponding to the mops p n x n 0 and q n x n 0 finally we show that if p n x n 0 is a semiclassical orthogonal polynomial sequence then so is q n x n 0 and in particular we analyze the classical case in detail

chebyshev polynomials and least squares estimation based on one dependent random variables abstract one dependent random variables appear in several fields of statistical work e g in time series analysis and sampling theory we consider such random variables y 1 y k k n with e yi i 1 k and regular tridiagonal covaria nce matrix the real parameter can be estimated by the method of least squares which leads to the best linear unbiased estimator uopt we give representations of uopt and v uopt in terms of chebyshev polynomials which turn out to be a helpful tool in the analysis of structure and properties of uopt using well known relations we give some more sum formulas and formulas concerning products of chebyshev polynomials which may also be of interest in other contexts

the inverse of banded matrices the inverses of r banded matrices for r 1 2 3 have been thoroughly investigated as one can see from the references we provide let b r n email protected email protected n be an nxn matrix of entries a j i email protected email protected r email protected email protected r with the remaining un indexed entries all zeros in this paper generalizing a method of mallik 1999 5 we give the lu factorization and the inverse of the matrix b r n if it exists our results are valid for an arbitrary square matrix taking r n and so we will give a new approach for computing the inverse of an invertible square matrix our method is based on hessenberg submatrices associated to b r n

eigenvalues of a certain class of tridiagonal matrices we make a short comment on a paper involving the minimal eigenvalues of a specialized version of 2 toeplitz tridiagonal matrices

fisher information kinetic energy and uncertainty relation inequalities by interpolating between fisher information and mechanical kinetic energy we introduce a general notion of kinetic energy with respect to a parameter of schrodinger wavefunctions from a statistical inference perspective kinetic energy is the sum of fisher information and an integral of a parametrized analogue of quantum mechanical current density related to phase a family of integral inequalities concerning kinetic energy and moments are established among which the cramer rao inequality and the weyl heisenberg inequality are special cases in particular the integral inequalities involving the negative order moments are relevant to the study of electron systems moreover by specifying the parameter to a scale we obtain a family of inequalities of uncertainty relation type which incorporate the position and momentum observables symmetrically in a single quantity

explicit inverse of a tridiagonal p r toeplitz matrix abstract we have named tridiagonal p r toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi periodic sequence d p j r d j so with period p n but multiplied by a real number r we present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse the techniques we use are related with the solution of boundary value problems associated to second order linear difference equations these boundary value problems can be expressed throughout the discrete schrodinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi periodic coefficients the conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix whereas the solutions of the boundary value problems provides the entries of the inverse matrix

inverses of k toeplitz matrices with applications to resonator arrays with multiple receivers abstract we find closed form algebraic formulas for the elements of the inverses of tridiagonal 2 and 3 toeplitz matrices which are symmetric and have constant upper and lower diagonals these matrices appear respectively as the impedance matrices of resonator arrays in which a receiver is placed over every 2 or 3 resonators consequently our formulas allow to compute the currents of a wireless power transfer system in closed form allowing for a simple exact and symbolic analysis thereof small numbers are chosen for illustrative purposes but the elementary linear algebra techniques used can be extended to k toeplitz matrices of this special form with k arbitrary hence resonator arrays with a receiver placed over every k resonators can be analysed in the same way

a short cut method for estimation in renewal processes this article proposes a simple noniterative estimator of the lifetime distribution from stationary renewal processes data which is a variation of the kaplan meier estimator the method is compared with the nonparametric maximum likelihood estimator using real and simulated data and the results show that as long as the censoring level is not too high the two estimates are remarkably close a heuristic asymptotic argument is given to support the simulation results and to justify the rationale behind the estimator the estimator s connection with the kaplan meier estimator is exploited to suggest a variance estimate and associated confidence interval which through a simulation study are found to be conservative

on the number of p vertices of some graphs abstract we provide positive answers to some open questions presented recently by kim and shader on a continuity like property of the p vertices of nonsingular matrices whose graph is a path a criterion for matrices associated with more general trees to have at most n 1 p vertices is established the cases of the cycles and stars are also analyzed several algorithms for generating matrices with a given number of p vertices are proposed

some integral identities and inequalities for entire functions and their application to the coherent state transform let be an entire function on cn and for any h 0 and r 0 define fr z r e 2 z 2h let d h denote h n times lebesgue measure on cn frs2 2 d h n sh frsd h from this and a logarithmic sobolev inequality we easily deduce qnq fr q pnp fr p for all 0 p q t8 where the lp norms are taken with respect to the measure d h above we apply these results to the study of the spaces ap consisting of all entire functions satisfying z pe 2 z 2h d h obtaining sharp bounds for some associated operators and proving denseness of analytic polynomials in ap for 1 p we then apply our results to the coherent state transform extending and simplifying some previously known results

fisher information matrix of husimi distribution we calculate the fisher information matrix of husimi distribution in the fock bargmann representation it turns out that the fisher information of the position and that of the momentum move in opposite directions and that a weighted trace of the fisher information matrix is a constant independent of the husimi distribution this may be interpreted as a kind of uncertainty relation in the spirit of heisenberg uncertainty principle from the statistical inference point of view

structured doubling algorithms for weakly stabilizing hermitian solutions of algebraic riccati equations in this paper we propose structured doubling algorithms for the computation of the weakly stabilizing hermitian solutions of the continuous and discrete time algebraic riccati equations respectively assume that the partial multiplicities of purely imaginary and unimodular eigenvalues if any of the associated hamiltonian and symplectic pencil respectively are all even and the c dare and the dual c dare have weakly stabilizing hermitian solutions with property p under these assumptions we prove that if these structured doubling algorithms do not break down then they converge to the desired hermitian solutions globally and linearly numerical experiments show that the structured doubling algorithms perform efficiently and reliably

explicit inverses of some tridiagonal matrices abstract we give explicit inverses of tridiagonal 2 toeplitz and 3 toeplitz matrices which generalize some well known results concerning the inverse of a tridiagonal toeplitz matrix

an informational characterization of schrodinger s uncertainty relations heisenberg s uncertainty relations employ commutators of observables to set fundamental limits on quantum measurement the information concerning incompatibility non commutativity of observables is well included but that concerning correlation is missing schrodinger s uncertainty relations remedy this defect by supplementing the correlation in terms of anti commutators however both heisenberg s uncertainty relations and schrodinger s uncertainty relations are expressed in terms of variances which are not good measures of uncertainty in general situations e g when mixed states are involved by virtue of the wigner yanase skew information we will establish an uncertainty relation along the spirit of schrodinger from a statistical inference perspective and propose a conjecture the result may be interpreted as a quantification of certain aspect of the celebrated wigner araki yanase theorem for quantum measurement which states that observables not commuting with a conserved quantity cannot be measured exactly

time reversible hamiltonian systems it is shown that transfer matrices satisfying g s g s g t t s have a minimal hamiltonian realization with an energy which is the sum of potential and kinetic energy yielding the time reversibility of the equations furthermore connections are made with an associated gradient system the theory is applied to electrical networks resulting in a characterization of lct networks

the eigenproblem of a tridiagonal 2 toeplitz matrix abstract the characteristic polynomial of a tridiagonal 2 toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point chebyshev recurrence relationship this is an extension of the well known result for a tridiagonal toeplitz matrix when the order of the matrix is odd the eigenvalues are found explicitly in terms of the chebyshev zeros the eigenvectors are found in terms of the polynomials satisfying the three point recurrence relationship

unifying some pell and fibonacci identities abstract in this short note we provide a unified approach to recent proofs for some identities on fibonacci and pell numbers we use chebyshev polynomials of second kind and a basic complex analysis result

explicit expression for powers of tridiagonal 2 toeplitz matrix of odd order abstract in this paper we give the eigenvalue decomposition for odd order tridiagonal 2 toeplitz matrix and derive the explicit expression for integer powers of such matrix

a new procedure for stochastic realization of spectral density matrices in this paper we consider the problem of obtaining a state space realization of a zero mean gaussian vector process a new algorithm is presented for the case in which the process is given in terms of its spectral density function contrary to the usual procedure followed which requires a partial fraction expansion the algorithm presented starts with a deterministic realization of the spectral density function itself

hamiltonian systems with a discrete symmetry abstract if m m is an antisymplectic involution of a symplectic manifold m then the fixed set of is a lagrangian submanifold l m moreover there exist cotangent bundle coordinates in a neighborhood of l in m such that in these coordinates maps a covector into its negative thus classical examples which have a discrete symmetry such as the restricted three body problems are locally like a reversible system

green matrices associated with generalized linear polyominoes a polyomino is an edge connected union of cells in the planar square lattice here we consider generalized linear polyominoes that is the polyominoes supported by an n a 2 lattice in this paper we obtain the green function and the kirchhoff index of a generalized linear polyomino as a perturbation of a 2n path by adding weighted edges between opposite vertices this approach deeply links generalized linear polyomino green functions with the inverse m matrix problem and especially with the so called green matrices