Bibliografie tematiche / Non asymptotic bounds

Letteratura scientifica selezionata sul tema "Non asymptotic bounds"

Autore: Grafiati

Pubblicato: 1 giugno 2024

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Articoli di riviste sul tema "Non asymptotic bounds":

Jiang, Yu Hang, Tong Liu, Zhiya Lou, Jeffrey S. Rosenthal, Shanshan Shangguan, Fei Wang e Zixuan Wu. "Markov Chain Confidence Intervals and Biases". International Journal of Statistics and Probability 11, n. 1 (21 dicembre 2021): 29. http://dx.doi.org/10.5539/ijsp.v11n1p29.

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We derive explicit asymptotic confidence intervals for any Markov chain Monte Carlo (MCMC) algorithm with finite asymptotic variance, started at any initial state, without requiring a Central Limit Theorem nor reversibility nor geometric ergodicity nor any bias bound. We also derive explicit non-asymptotic confidence intervals assuming bounds on the bias or first moment, or alternatively that the chain starts in stationarity. We relate those non-asymptotic bounds to properties of MCMC bias, and show that polynomially ergodicity implies certain bias bounds. We also apply our results to several numerical examples. It is our hope that these results will provide simple and useful tools for estimating errors of MCMC algorithms when CLTs are not available.

Zhou, Lin, e Mehul Motani. "Non-Asymptotic Converse Bounds and Refined Asymptotics for Two Source Coding Problems". IEEE Transactions on Information Theory 65, n. 10 (ottobre 2019): 6414–40. http://dx.doi.org/10.1109/tit.2019.2920893.

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Xia, Dong. "Non-asymptotic bounds for percentiles of independent non-identical random variables". Statistics & Probability Letters 152 (settembre 2019): 111–20. http://dx.doi.org/10.1016/j.spl.2019.04.018.

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Menozzi, Stéphane, e Vincent Lemaire. "On Some non Asymptotic Bounds for the Euler Scheme". Electronic Journal of Probability 15 (2010): 1645–81. http://dx.doi.org/10.1214/ejp.v15-814.

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Yang, Xiaowei, Lu Pan, Kun Cheng e Chao Liu. "Optimal Non-Asymptotic Bounds for the Sparse β Model". Mathematics 11, n. 22 (17 novembre 2023): 4685. http://dx.doi.org/10.3390/math11224685.

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This paper investigates the sparse β model with 𝓁1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis.

Raj Jhunjhunwala, Prakirt, Daniela Hurtado-Lange e Siva Theja Maguluri. "Exponential Tail Bounds on Queues: A Confluence of Non- Asymptotic Heavy Traffic and Large Deviations". ACM SIGMETRICS Performance Evaluation Review 51, n. 4 (22 febbraio 2024): 18–19. http://dx.doi.org/10.1145/3649477.3649488.

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In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we focus on establishing bounds for the tail probabilities of queue lengths. We examine queueing systems under Heavy Traffic (HT) conditions and provide exponentially decaying bounds for the probability P(∈q > x), where ∈ is the HT parameter denoting how far the load is from the maximum allowed load. Our bounds are not limited to asymptotic cases and are applicable even for finite values of ∈, and they get sharper as ∈ - 0. Consequently, we derive non-asymptotic convergence rates for the tail probabilities. Furthermore, our results offer bounds on the exponential rate of decay of the tail, given by -1/2 log P(∈q > x) for any finite value of x. These can be interpreted as non-asymptotic versions of Large Deviation (LD) results. To obtain our results, we use an exponential Lyapunov function to bind the moment-generating function of queue lengths and apply Markov's inequality. We demonstrate our approach by presenting tail bounds for a continuous time Join-the-shortest queue (JSQ) system.

Függer, Matthias, Thomas Nowak e Manfred Schwarz. "Tight Bounds for Asymptotic and Approximate Consensus". Journal of the ACM 68, n. 6 (31 dicembre 2021): 1–35. http://dx.doi.org/10.1145/3485242.

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Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in human-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. We study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP’16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks.

Gu, Yujie, e Ofer Shayevitz. "On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel". Entropy 23, n. 11 (15 novembre 2021): 1518. http://dx.doi.org/10.3390/e23111518.

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We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon’s vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which, in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs, and show that this bound can be achieved in certain cases.

Lim, Fabian, e Vladimir Stojanovic. "On U-Statistics and Compressed Sensing II: Non-Asymptotic Worst-Case Analysis". Signal Processing, IEEE Transactions on 61, n. 10 (aprile 2013): 2486–97. http://dx.doi.org/10.1109/tsp.2013.2255041.

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In another related work, U-statistics were used for non-asymptotic average-case analysis of random compressed sensing matrices. In this companion paper the same analytical tool is adopted differently-here we perform non-asymptotic worst-case analysis. Simple union bounds are a natural choice for worst-case analyses, however their tightness is an issue (and questioned in previous works). Here we focus on a theoretical U-statistical result, which potentially allows us to prove that these union bounds are tight. To our knowledge, this kind of (powerful) result is completely new in the context of CS. This general result applies to a wide variety of parameters, and is related to (Stein-Chen) Poisson approximation. In this paper, we consider i) restricted isometries, and ii) mutual coherence. For the bounded case, we show that -th order restricted isometry constants have tight union bounds, when the measurements m = O (k(1.5(+ log(n/k))). Here, we require the restricted isometries to grow linearly in , however we conjecture that this result can be improved to allow them to be fixed. Also, we show that mutual coherence (with the standard estimate √(4 log n)/m) have very tight union bounds. For coherence, the normalization complicates general discussion, and we consider only Gaussian and Bernoulli cases here.

Cheng, Xu, Zhipeng Liao e Ruoyao Shi. "On uniform asymptotic risk of averaging GMM estimators". Quantitative Economics 10, n. 3 (2019): 931–79. http://dx.doi.org/10.3982/qe711.

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This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite‐sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non‐Gaussian semiparametric nonlinear models.

Più fonti

Tesi sul tema "Non asymptotic bounds":

Minsker, Stanislav. "Non-asymptotic bounds for prediction problems and density estimation". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44808.

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This dissertation investigates the learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary classification problem in the framework of active learning. Given a random couple (X,Y) with unknown distribution P, the goal of binary classification is to predict a label Y based on the observation X. Prediction rule is constructed from a sequence of observations sampled from P. The concept of active learning can be informally characterized as follows: on every iteration, the algorithm is allowed to request a label Y for any instance X which it considers to be the most informative. The contribution of this work consists of two parts: first, we provide the minimax lower bounds for the performance of active learning methods. Second, we propose an active learning algorithm which attains nearly optimal rates over a broad class of underlying distributions and is adaptive with respect to the unknown parameters of the problem. The second part of this thesis is related to sparse recovery in the framework of dictionary learning. Let (X,Y) be a random couple with unknown distribution P. Given a collection of functions H, the goal of dictionary learning is to construct a prediction rule for Y given by a linear combination of the elements of H. The problem is sparse if there exists a good prediction rule that depends on a small number of functions from H. We propose an estimator of the unknown optimal prediction rule based on penalized empirical risk minimization algorithm. We show that the proposed estimator is able to take advantage of the possible sparse structure of the problem by providing probabilistic bounds for its performance.

Schweizer, Nikolaus [Verfasser]. "Non-asymptotic Error Bounds for Sequential MCMC Methods / Nikolaus Schweizer". Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1044081546/34.

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Donier-Meroz, Etienne. "Graphon estimation in bipartite networks". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAG010.

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De nombreux ensembles de données peuvent être représentés sous forme d'une matrice dont les entrées représentent les interactions entre deux entités de natures différentes. Ces matrices sont appelées matrices d'adjacence de graphes bipartites. Dans notre travail, nous faisons l'hypothèse que ces interactions sont déterminées par des variables latentes non observables.Dans un premier temps, notre objectif est d'estimer l'espérance conditionnelle de la matrice de données sachant les variables non observables, en supposant que les entrées de la matrice sont i.i.d. Ce problème peut être formulé comme l'estimation d'une fonction bivariée appelée graphon. Dans notre étude, nous nous concentrons sur deux cas, les graphons constants par morceaux et les graphons Hölder.Nous démontrons des bornes de risque pour l'estimateur des moindres carrés, et nous proposons une adaptation de l'algorithme de Lloyd pour calculer une approximation de cet estimateur et nous présentons les résultats d'expériences numériques pour évaluer les performances de ces méthodes.Dans un deuxième temps, nous abordons les limites du cadre précédent, qui peut ne pas être adapté pour modéliser des situations avec des degrés de sommet bornés. Par conséquent, nous étendons notre étude à l'hypothèse de l'indépendance relaxée, où seules les lignes de la matrice d'adjacence sont supposées indépendantes. Dans ce contexte, nous nous concentrons spécifiquement sur les graphons constants par morceaux
Many real-world datasets can be represented as matrices where the entries represent interactions between two entities of different natures. These matrices are commonly known as adjacency matrices of bipartite graphs. In our work, we make the assumption that these interactions are determined by unobservable latent variables.Firstly, our main objective is to estimate the conditional expectation of the data matrix given the unobservable variables under the assumption that matrix entries are i.i.d. This estimation problem can be framed as estimating a bivariate function known as a graphon. In our study, we focus on two cases: piecewise constant graphons and Hölder-continuous graphons.We derive finite sample risk bounds for the least squares estimator. Additionally, we propose an adaptation of Lloyd's algorithm to compute an approximation this estimator and provide results from numerical experiments to evaluate the performance of these methods.Secondly, we address the limitations of the previous framework, which may not be suitable for modeling situations with bounded degrees of vertices, among other scenarios. Therefore, we extend our study to the relaxed independence assumption, where only the rows of the adjacency matrix are assumed to be independent. In this context, we specifically focus on piecewise constant graphons

Bacharach, Lucien. "Caractérisation des limites fondamentales de l'erreur quadratique moyenne pour l'estimation de signaux comportant des points de rupture". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS322/document.

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Cette thèse porte sur l'étude des performances d'estimateurs en traitement du signal, et s'attache en particulier à étudier les bornes inférieures de l'erreur quadratique moyenne (EQM) pour l'estimation de points de rupture, afin de caractériser le comportement d'estimateurs, tels que celui du maximum de vraisemblance (dans le contexte fréquentiste), mais surtout du maximum a posteriori ou de la moyenne conditionnelle (dans le contexte bayésien). La difficulté majeure provient du fait que, pour un signal échantillonné, les paramètres d'intérêt (à savoir les points de rupture) appartiennent à un espace discret. En conséquence, les résultats asymptotiques classiques (comme la normalité asymptotique du maximum de vraisemblance) ou la borne de Cramér-Rao ne s'appliquent plus. Quelques résultats sur la distribution asymptotique du maximum de vraisemblance provenant de la communauté mathématique sont actuellement disponibles, mais leur applicabilité à des problèmes pratiques de traitement du signal n'est pas immédiate. Si l'on décide de concentrer nos efforts sur l'EQM des estimateurs comme indicateur de performance, un travail important autour des bornes inférieures de l'EQM a été réalisé ces dernières années. Plusieurs études ont ainsi permis de proposer des inégalités plus précises que la borne de Cramér-Rao. Ces dernières jouissent en outre de conditions de régularité plus faibles, et ce, même en régime non asymptotique, permettant ainsi de délimiter la plage de fonctionnement optimal des estimateurs. Le but de cette thèse est, d'une part, de compléter la caractérisation de la zone asymptotique (en particulier lorsque le rapport signal sur bruit est élevé et/ou pour un nombre d'observations infini) dans un contexte d'estimation de points de rupture. D'autre part, le but est de donner les limites fondamentales de l'EQM d'un estimateur dans la plage non asymptotique. Les outils utilisés ici sont les bornes inférieures de l’EQM de la famille Weiss-Weinstein qui est déjà connue pour être plus précise que la borne de Cramér-Rao dans les contextes, entre autres, de l’analyse spectrale et du traitement d’antenne. Nous fournissons une forme compacte de cette famille dans le cas d’un seul et de plusieurs points de ruptures puis, nous étendons notre analyse aux cas où les paramètres des distributions sont inconnus. Nous fournissons également une analyse de la robustesse de cette famille vis-à-vis des lois a priori utilisées dans nos modèles. Enfin, nous appliquons ces bornes à plusieurs problèmes pratiques : données gaussiennes, poissonniennes et processus exponentiels
This thesis deals with the study of estimators' performance in signal processing. The focus is the analysis of the lower bounds on the Mean Square Error (MSE) for abrupt change-point estimation. Such tools will help to characterize performance of maximum likelihood estimator in the frequentist context but also maximum a posteriori and conditional mean estimators in the Bayesian context. The main difficulty comes from the fact that, when dealing with sampled signals, the parameters of interest (i.e., the change points) lie on a discrete space. Consequently, the classical large sample theory results (e.g., asymptotic normality of the maximum likelihood estimator) or the Cramér-Rao bound do not apply. Some results concerning the asymptotic distribution of the maximum likelihood only are available in the mathematics literature but are currently of limited interest for practical signal processing problems. When the MSE of estimators is chosen as performance criterion, an important amount of work has been provided concerning lower bounds on the MSE in the last years. Then, several studies have proposed new inequalities leading to tighter lower bounds in comparison with the Cramér-Rao bound. These new lower bounds have less regularity conditions and are able to handle estimators’ MSE behavior in both asymptotic and non-asymptotic areas. The goal of this thesis is to complete previous results on lower bounds in the asymptotic area (i.e. when the number of samples and/or the signal-to-noise ratio is high) for change-point estimation but, also, to provide an analysis in the non-asymptotic region. The tools used here will be the lower bounds of the Weiss-Weinstein family which are already known in signal processing to outperform the Cramér-Rao bound for applications such as spectral analysis or array processing. A closed-form expression of this family is provided for a single and multiple change points and some extensions are given when the parameters of the distributions on each segment are unknown. An analysis in terms of robustness with respect to the prior influence on our models is also provided. Finally, we apply our results to specific problems such as: Gaussian data, Poisson data and exponentially distributed data

Brunnbauer, Michael. "Topological properties of asymptotic invariants and universal volume bounds". Diss., lmu, 2008. http://nbn-resolving.de/urn:nbn:de:bvb:19-87504.

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El, Korso Mohammed Nabil. "Analyse de performances en traitement d'antenne : bornes inférieures de l'erreur quadratique moyenne et seuil de résolution limite". Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112074/document.

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Ce manuscrit est dédié à l’analyse de performances en traitement d’antenne pour l’estimation des paramètres d’intérêt à l’aide d’un réseau de capteurs. Il est divisé en deux parties :– Tout d’abord, nous présentons l’étude de certaines bornes inférieures de l’erreur quadratique moyenne liées à la localisation de sources dans le contexte champ proche. Nous utilisons la borne de Cramér-Rao pour l’étude de la zone asymptotique (notamment en terme de rapport signal à bruit avec un nombre fini d’observations). Puis, nous étudions d’autres bornes inférieures de l’erreur quadratique moyenne qui permettent de prévoir le phénomène de décrochement de l’erreur quadratique moyenne des estimateurs (on cite, par exemple, la borne de McAulay-Seidman, la borne de Hammersley-Chapman-Robbins et la borne de Fourier Cramér-Rao).– Deuxièmement, nous nous concentrons sur le concept du seuil statistique de résolution limite, c’est-à-dire, la distance minimale entre deux signaux noyés dans un bruit additif qui permet une ”correcte” estimation des paramètres. Nous présentons quelques applications bien connues en traitement d’antenne avant d’étendre les concepts existants au cas de signaux multidimensionnels. Par la suite, nous étudions la validité de notre extension en utilisant un test d’hypothèses binaire. Enfin, nous appliquons notre extension à certains modèles d’observation multidimensionnels
This manuscript concerns the performance analysis in array signal processing. It can bedivided into two parts :- First, we present the study of some lower bounds on the mean square error related to the source localization in the near eld context. Using the Cramér-Rao bound, we investigate the mean square error of the maximum likelihood estimator w.r.t. the direction of arrivals in the so-called asymptotic area (i.e., for a high signal to noise ratio with a nite number of observations.) Then, using other bounds than the Cramér-Rao bound, we predict the threshold phenomena.- Secondly, we focus on the concept of the statistical resolution limit (i.e., the minimum distance between two closely spaced signals embedded in an additive noise that allows a correct resolvability/parameter estimation.) We de ne and derive the statistical resolution limit using the Cramér-Rao bound and the hypothesis test approaches for the mono-dimensional case. Then, we extend this concept to the multidimensional case. Finally, a generalized likelihood ratio test based framework for the multidimensional statistical resolution limit is given to assess the validity of the proposed extension

Pinto, Manuel. "Des inegalites fonctionnelles et leurs applications". Université Louis Pasteur (Strasbourg) (1971-2008), 1988. http://www.theses.fr/1988STR13097.

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Etude du comportement asymptotique des solutions des equations differentielles non lineaires. Solution d'une inegalite du type de gronwall-bellman-bihari avec un nombre fini quelconque de non-linearites. Applications : recherche des solutions asymptotiques et asymptotiquement polynomiales, stabilite des h-systemes en variation soumise a des perturbations integrales; solutions bornees des equations differentielles dans un espace de banach et equilibre asymptotique. Version discrete et multivariable de l'inegalite fonctionnelle resolue

Hadiji, Hédi. "On some adaptivity questions in stochastic multi-armed bandits". Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM021.

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Cette thèse s'inscrit dans le domaine des statistiques séquentielles. Le cadre principal étudié est celui des bandits stochastiques à plusieurs bras, cadre idéal qui modélise le dilemme exploration-exploitation face à des choix répétés. La thèse est composée de quatre chapitres, précédés d'une introduction. Dans la première partie du corps de la thèse, on présente un nouvel algorithme capable d'atteindre des garanties optimales à la fois d'un point de vue distribution-dépendent et distribution-free. Les deux chapitres suivants sont consacrés à des questions dites d'adaptation. D'abord, on propose un algorithme capable de s'adapter à la régularité inconnue dans des problèmes de bandits continus, mettant en évidence le coût polynomial de l'adaptation en bandits continus. Ensuite, on considère un problème d'adaptation au supports pour des problèmes de bandits à K bras, à distributions de paiements bornés dans des intervalles inconnus. Enfin, dans un dernier chapitre un peu à part, on étudie un cadre légèrement différent de bandits préservant la diversité. On montre que le regret optimal dans ce cadre croît à des vitesses différentes des vitesses classiques, avec notamment la possibilité d'atteindre un regret constant sous certaines hypothèses
The main topics adressed in this thesis lie in the general domain of sequential learning, and in particular stochastic multi-armed bandits. The thesis is divided into four chapters and an introduction. In the first part of the main body of the thesis, we design a new algorithm achieving, simultaneously, distribution-dependent and distribution-free optimal guarantees. The next two chapters are devoted to adaptivity questions. First, in the context of continuum-armed bandits, we present a new algorithm which, for the first time, does not require the knowledge of the regularity of the bandit problem it is facing. Then, we study the issue of adapting to the unknown support of the payoffs in bounded K-armed bandits. We provide a procedure that (almost) obtains the same guarantees as if it was given the support in advance. In the final chapter, we study a slightly different bandit setting, designed to enforce diversity-preserving conditions on the strategies. We show that the optimal regert in this setting at a speed that is quite different from the traditional bandit setting. In particular, we observe that bounded regret is possible under some specific hypotheses

Hussain, Zahir M. "Adaptive instantaneous frequency estimation: Techniques and algorithms". Thesis, Queensland University of Technology, 2002. https://eprints.qut.edu.au/36137/7/36137_Digitised%20Thesis.pdf.

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This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Capitoli di libri sul tema "Non asymptotic bounds":

Fujikoshi, Yasunori, e Vladimir V. Ulyanov. "Non-Asymptotic Bounds". In Non-Asymptotic Analysis of Approximations for Multivariate Statistics, 1–4. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-13-2616-5_1.

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Fujikoshi, Yasunori, e Vladimir V. Ulyanov. "General Approach to Constructing Non-Asymptotic Bounds". In Non-Asymptotic Analysis of Approximations for Multivariate Statistics, 117–30. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-13-2616-5_11.

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van de Geer, Sara A. "On non-asymptotic bounds for estimation in generalized linear models with highly correlated design". In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 121–34. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007. http://dx.doi.org/10.1214/074921707000000319.

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Kahn, David M., e Jan Hoffmann. "Exponential Automatic Amortized Resource Analysis". In Lecture Notes in Computer Science, 359–80. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_19.

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Abstract (sommario):

AbstractAutomatic amortized resource analysis (AARA) is a type-based technique for inferring concrete (non-asymptotic) bounds on a program’s resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. This paper presents and extension of AARA to exponential bounds that preserves the benefits of the technique, such as compositionality and efficient type inference based on linear constraint solving. A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. To formalize the similarities with the existing analyses, the paper presents a general methodology for AARA that is instantiated to the polynomial version, the exponential version, and a combined system with potential functions that are formed by products of Stirling numbers and binomial coefficients. The soundness of exponential AARA is proved with respect to an operational cost semantics and the analysis of representative example programs demonstrates the effectiveness of the new analysis.

Sjöstrand, Johannes. "Proof I: Upper Bounds". In Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations, 329–61. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10819-9_16.

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Sjöstrand, Johannes. "Proof II: Lower Bounds". In Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations, 363–407. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10819-9_17.

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Sjöstrand, Johannes. "From Resolvent Estimates to Semigroup Bounds". In Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations, 211–17. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10819-9_11.

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Akahira, Masafumi, e Kei Takeuchi. "Supplement The Bound for the Asymptotic Distribution of Estimators when the Maximum Order of Consistency Depends on the Parameter". In Non-Regular Statistical Estimation, 166–73. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-2554-6_8.

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Nguyen, TrungTin, Dung Ngoc Nguyen, Hien Duy Nguyen e Faicel Chamroukhi. "A Non-asymptotic Risk Bound for Model Selection in a High-Dimensional Mixture of Experts via Joint Rank and Variable Selection". In Lecture Notes in Computer Science, 234–45. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-8391-9_19.

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FUJIKOSHI, Y. "Non-uniform Error Bounds for Asymptotic Expansions of Scale Mixtures of Distributions". In Multivariate Statistics and Probability, 194–205. Elsevier, 1989. http://dx.doi.org/10.1016/b978-0-12-580205-5.50020-3.

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Atti di convegni sul tema "Non asymptotic bounds":

Matsuta, Tetsunao, e Tomohiko Uyematsu. "Non-asymptotic bounds for fixed-length lossy compression". In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282768.

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Verdu, Sergio. "Non-asymptotic achievability bounds in multiuser information theory". In 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2012. http://dx.doi.org/10.1109/allerton.2012.6483192.

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Zhang, Jianqiu. "Non-Asymptotic Capacity Lower Bounds for Non-coherent SISO Channels". In 2006 40th Annual Conference on Information Sciences and Systems. IEEE, 2006. http://dx.doi.org/10.1109/ciss.2006.286409.

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Wei, Jiahui, Elsa Dupraz e Philippe Mary. "Asymptotic and Non-Asymptotic Rate-Loss Bounds for Linear Regression with Side Information". In 2023 31st European Signal Processing Conference (EUSIPCO). IEEE, 2023. http://dx.doi.org/10.23919/eusipco58844.2023.10289952.

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Fort, G., e E. Moulines. "The Perturbed Prox-Preconditioned Spider Algorithm: Non-Asymptotic Convergence Bounds". In 2021 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2021. http://dx.doi.org/10.1109/ssp49050.2021.9513846.

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Liebeherr, Jorg, Almut Burchard e Florin Ciucu. "Non-asymptotic Delay Bounds for Networks with Heavy-Tailed Traffic". In IEEE INFOCOM 2010 - IEEE Conference on Computer Communications. IEEE, 2010. http://dx.doi.org/10.1109/infcom.2010.5461913.

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Hayashi, Masahito, e Shun Watanabe. "Non-asymptotic bounds on fixed length source coding for Markov chains". In 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2013. http://dx.doi.org/10.1109/allerton.2013.6736617.

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Heimann, Ron, Amir Leshem, Ephraim Zehavi e Anthony J. Weiss. "Non-asymptotic performance bounds of eigenvalue based detection of signals in non-Gaussian noise". In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472215.

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Watanabe, Shun, Shigeaki Kuzuoka e Vincent Y. F. Tan. "Non-asymptotic and second-order achievability bounds for source coding with side-information". In 2013 IEEE International Symposium on Information Theory (ISIT). IEEE, 2013. http://dx.doi.org/10.1109/isit.2013.6620787.

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Alaeddini, Atiye, Siavash Alemzadeh, Afshin Mesbahi e Mehran Mesbahi. "Linear Model Regression on Time-series Data: Non-asymptotic Error Bounds and Applications". In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619074.

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Rapporti di organizzazioni sul tema "Non asymptotic bounds":

Petrova, Katerina. On the Validity of Classical and Bayesian DSGE-Based Inference. Federal Reserve Bank of New York, gennaio 2024. http://dx.doi.org/10.59576/sr.1084.

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Abstract (sommario):

This paper studies large sample classical and Bayesian inference in a prototypical linear DSGE model and demonstrates that inference on the structural parameters based on a Gaussian likelihood is unaffected by departures from Gaussianity of the structural shocks. This surprising result is due to a cancellation in the asymptotic variance resulting into a generalized information equality for the block corresponding to the structural parameters. The underlying reason for the cancellation is the certainty equivalence property of the linear rational expectation model. The main implication of this result is that classical and Bayesian Gaussian inference achieve a semi-parametric efficiency bound and there is no need for a “sandwich-form” correction of the asymptotic variance of the structural parameters. Consequently, MLE-based confidence intervals and Bayesian credible sets of the deep parameters based on a Gaussian likelihood have correct asymptotic coverage even when the structural shocks are non-Gaussian. On the other hand, inference on the reduced-form parameters characterizing the volatility of the shocks is invalid whenever the structural shocks have a non-Gaussian density and the paper proposes a simple Metropolis-within-Gibbs algorithm that achieves correct large sample inference for the volatility parameters.