We study the asymptotic null spectrum of Gaussian-weighted tests of univariate normality with estimated location and scale. Closed Hermite coefficients give equations both away from and at the unperturbed poles. Every positive eigenvalue of the fully standardized covariance is simple, and the odd and even eigenvalues alternate strictly. For each unperturbed even pole except the largest, there is exactly one weight parameter at which it belongs to the perturbed even spectrum. These parameters are strictly ordered and converge to the boundary of the parameter interval. A signed total-positivity argument proves simplicity more generally for consecutive Gaussian covariance corrections and positive even integrable weights. We also derive the limiting quadratic forms directly from degenerate kernels at standardized observations. A derivative summability condition controls the complete spectral tail, including signed kernels, and is verified for characteristic-function kernels with a finite fourth weight moment. A real Hilbert-space factorization identifies the observation and Fourier spectra. Numerical calculations assess asymptotic calibration.
N. Gkoumas, N. Papadatos, S. Trevezas· 0 citations
We develop nonparametric inference for reliability indicators of discrete-time semi-Markov systems from independent trajectories observed over a common fixed horizon. Augmenting the physical state by the backward recurrence time yields a finite coupled Markov representation on the observed age range. We distinguish the resulting age-restricted failure-or-exit time from calendar truncation, since these two finite-horizon quantities coincide only in special cases. The framework covers restricted factorial moments and moment characteristics, calendar-truncated failure-time summaries, and the discrete-time intensity of the hitting time. Under explicit row-exposure conditions, strong consistency and joint asymptotic normality are established for the empirical initial law, the required transition rows and the corresponding plug-in functionals. The Gaussian random-matrix representation gives pointwise and joint covariance formulas, simultaneous confidence envelopes, Wald procedures for linear summaries, and curvature-adjusted Gaussian approximations. Restriction diagnostics and a target-specific horizon-selection rule based on exposure, boundary interaction and nested-horizon stability are developed separately. Numerical experiments assess the inferential formulas and the diagnostics, while a complete-case illustration from the European Group for Blood and Marrow Transplantation (EBMT) reports calendar-truncated failure-time summaries and finite-dimensional hitting intensities.
S. Trevezas, M. Hamdaoui, Irène Votsi· Methodology and Computing in...· 0 citations
We develop a discrete Markov renewal theory on a standard Borel state space, with vector-valued sojourn times and lower-rectangle observation on $\N^d$. The Markov renewal potential is a kernel-valued convolution resolvent and yields unified representations for semi-Markov transitions, first-passage laws, occupation measures and rewards. The semi-Markov field observed on the partially ordered lattice is generally not Markov. We identify its canonical Markovian augmentation through the backward recurrence vector and give a lumpability criterion for the exceptional cases in which the augmentation can be projected back to the original state space. The lower-rectangle order leads to a stratified inverse-renewal theory: the direction simplex is decomposed into rate-determining cells, with Gaussian limits on cells having a unique active coordinate and minima of correlated Gaussian fields on their interfaces. We establish functional inverse limits, critical-interface limits and logarithmic estimates for inverse deviations. Exact-time potentials are obtained from an operator-theoretic local theorem for Fourier--Laplace perturbations of Markov-additive kernels, while a regenerative theorem gives the corresponding arithmetic lattice-class form. The results connect Markov renewal equations, multiparameter Markov structure and the local asymptotic geometry induced by rectangular observation.
In this work, we develop a unified matrix-level asymptotic calculus for plug-in non-parametric maximum likelihood estimators in finite Markov models. Starting from the asymptotic distribution of the estimated transition matrix, the limiting object is kept in its natural matrix form as a Gaussian random matrix, while the corresponding row-wise vector representation remains immediately available. The main point is that the stochastic constraints of the transition matrix need not be removed by a minimal parametrization: they are carried by the tangent directions and by the covariance structure of the limiting Gaussian matrix, whereas the relevant differentials are computed directly in matrix spaces. A single stochastic calculus theorem gives first-order limit distributions, finite-order developments for sufficiently differentiable functionals, and analytic expansions when the functional is analytic. This provides a common source for asymptotic formulas for matrix powers, stationary characteristics, finite-dimensional curves of Markov characteristics, additive-functional variances, entropy-type quantities and reliability indicators. The resulting covariance operators lead directly to confidence intervals, confidence regions, simultaneous finite-dimensional bands and Wald-type tests. Since the derivations are expressed through matrix products and Kronecker representations rather than coordinate-wise calculations, the method also gives substantial simplifications and, in many cases, computational gains. The second-order terms identify curvature corrections of smooth functionals and provide refined approximations whenever higher-order information is useful.
G. Gavrilopoulos, Samis Trevezas, Irène Votsi· 0 citations
An exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes is developed, showing how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion.
Vasileios E. Papageorgiou, Irène Votsi, S. Trevezas· 0 citations
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