Strong Normalization Research Articles

Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

Nonparametric Estimation of Distribution Function Under Right Random Censoring Based on Presmoothed Relative-Risk Function

In this article the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on conception of presmoothed estimation of relative-risk function is discussed. A strong uniform approximation of estimator by weighted sum of random functions is proved. As result the strong uniform consistency and asymptotical normality of estimator are also established. Some applications in parametric estimation problems are considered.

An indirect proof for the asymptotic properties of VARMA model estimators

Strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters of a causal, invertible, and identifiable vector autoregressive-moving average (VARMA) model are established in an indirect way. The proof is based on similar results for a much wider class of VARMA models with time-dependent coefficients, hence in the context of non-stationary and heteroscedastic time series. For that reason, the proof avoids spectral analysis arguments and does not make use of ergodicity. The results presented are also applicable to ARMA models.

Type inhabitation of atomic polymorphism is undecidable

Abstract Atomic polymorphism $\mathbf{F_{at}}$ is a restriction of Girard and Reynold’s system $\mathbf{F} $(or $\lambda 2$) which was first introduced in Ferreira [ 2] in the context of a philosophical commentary on predicativism. $\lambda 2$ is a well-known and powerful formal tool for studying polymorphic functional programming languages and formal methods in program specification and development, but its computational power far exceeds the recursive level of interest in applications. Hence, the interest of studying subsystems of $\lambda 2$ with weaker computational power. $\mathbf{F_{at}}$ is defined by restricting instantiation to atomic variables only. It turns out that the type system is still sufficiently powerful to possess embeddings of full intuitionistic propositional calculus [ 3, 4], and since the calculus has fewer connectives and strong normalizability is simple to prove [ 3], this result allows us to circumvent many of the extra computational complexities present when dealing with the proof theory of IPC. It is natural to inquire whether type inhabitation, i.e. provability in the corresponding fragment of second-order intuitionistic propositional logic, is decidable or not and in general to see whether the negative results involving the undecidability of type inhabitation, typability and type-checking for $\mathbf{F}$ still hold in this fragment. A further theme would be to study the result of adding type constructors, recursors or even dependent types to $\mathbf{F_{at}}$. In this paper, we show that type inhabitation for $\mathbf{F_{at}}$ is undecidable by codifying within it an undecidable fragment of first-order intuitionistic predicate calculus, adapting and modifying the technique of Urzyczyn’s [ 1, 7] purely syntactic proof of the undecidability of type inhabitation for $\mathbf{F}$.

Closed-form estimators and bias-corrected estimators for the Nakagami distribution

The Nakagami distribution is widely applied in various areas such as communicational engineering, medical imaging, multimedia, among others. New MLE-like estimators in closed-form are proposed for the Nakagami parameters through the likelihood function of the generalized Nakagami distribution, which contains the Nakagami distribution as a special case. For the MLE-like estimators of the Nakagami distribution, the scale parameter (ω) estimator is the same as its maximum likelihood estimator (MLE) and the shape parameter (μ) estimator performs close to the corresponding MLE. Strong consistency and asymptotic normality of the MLE-like estimators are confirmed in large-size samples. To reduce the bias in the samples with small sizes, four bias-corrected estimators of the shape parameter (μˆBC1, μˆBC2, μˆBC3, and μˆBC4) are developed based on its MLE-like estimator. The second bias-corrected estimator μˆBC2 is asymptotically unbiased and consequently, the third one μˆBC3 and fourth one μˆBC4 are also asymptotically unbiased because they are the approximations of the μˆBC2. Simulation studies and a real data example suggest that four bias-corrected estimators, especially the latter three, significantly improve the small-sample performance.

Identification of Intertemporal Preferences From Choice Set Variation

The paper provides conditions to identify the discount factor(s) and utility function in a infinite-horizon dynamic discrete choice model variation in choice sets over time. We show that if current choices or states are informative about the choice set the agent will face in the future, then the discount factor and utility are identified without any strong normalization. These identification results hold in both the exponential discounting model and, if the choice set provides a form of pre-commitment, the quasi-hyperbolic discounting model. Identifying the discount factor and utility allows us to identify the counterfactual policies which often are the objects of interest in dynamic discrete-choice analysis, but which are not generally identified.

Грассманоподобное многообразие центрированных плоскостей, когда центр описывает поверхность

We continue to study of the Grassmann-like manifold of -centered planes. A special case is considered when the center de­scribes an -dimensional surface . We will denote this mani­fold by . An analogue of the strong Norden normalization of the manifold is realized. It is proved that this normalization induces a connection in the bundle associated with the manifold . A geometric characteristic of this connection is given with the help of parallel displacements. In our research we use the Cartan method of external forms and the group-theoretical method of Laptev. These methods are used by many geometers and physicists. The Grassmann-like manifold is closely related to such a well-known and popular manifold as the Grassmann manifold. The Grassmann mani­fold is an example of a homogeneous space and forms an important fun­damental class of projective manifolds, and the projective space itself can be represented as a Grassmann manifold.

Term-Space Semantics of Typed Lambda Calculus

Barendregt gave a sound semantics of the simple type assignment system λ → by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.

Least squares estimator for a class of subdiffusion processes

In this article, we consider the parameter estimation problem for a class of subdiffusion processes which are characterized by the time-changed Ornstein–Uhlenbeck processes. Least squares method is used to obtain the estimator for the drift coefficient. First, we get the strong consistency, asymptotical normality and asymptotical mixed normality for the estimator on the condition that we can observe the process continuously. After that, weak consistent and asymptotic properties are derived basing on discrete observations when the time-change process is an inverse -stable () subordinator.

Nonlinear least squares estimation of the periodic EXPAR(1) model

In this paper, we study the strong consistency and asymptotic normality properties of nonlinear least squares (NLS) estimator of the periodic model. The general statistical literature on estimation of nonlinear models of Gallant and White is used. Simulation study and one real example are given to assess the performance of this NLS.

On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

ABSTRACT One-step Gauss-Newton estimators for causal and invertible autoregressive moving-average (ARMA) time series models with an unknown mean are considered. A proof of the strong consistency and asymptotic normality of these estimators is provided. In a simulation study, their empirical properties are illustrated in ARMA models and compared to a other estimators: the estimators based on the innovations algorithm procedure, the estimators based on the spectral methods of [Krampe J, Kreiss J-P, Paparoditis E. Estimated Wold representation and spectral-density-driven bootstrap for time series. J R Stat Soc: Ser B (Statist Method). 2018;80:703–726.], and the one-step Gauss-Newton estimators using these methods as preliminary estimators. In the order-one moving-average model, we included the estimator based on the method of moments. The sample mean is used as a preliminary estimator to estimate the mean. These estimators are compared empirically to the maximum Gaussian likelihood estimator with respect to exact biases and mean squared errors.

Strong Normalization for the Simply-Typed Lambda Calculus in Constructive Type Theory Using Agda

We consider a pre-existing formalization in Constructive Type Theory of the pure Lambda Calculus in its presentation in first order syntax with only one sort of names and alpha-conversion based upon multiple substitution, as well as of the system of assignment of simple types to terms. On top of it, we formalize a slick proof of strong normalization given by Joachimski and Matthes whose main lemma proceeds by complete induction on types and subordinate induction on a characterization of the strongly normalizing terms which is in turn proven sound with respect to their direct definition as the accessible part of the relation of one-step beta reduction. The proof of strong normalization itself is thereby allowed to consist just of a direct induction on the type system. The whole development has been machine-checked using the system Agda. We assess merits and drawbacks of the approach.

METHOD OF MOMENTS ESTIMATION FOR LÉVY-DRIVEN ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODELS

This paper studies the parameter estimation for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. We propose computationally efficient estimators based on the method of moments that are robust to model misspecification. We develop an analytical framework that enables closed-form representation of model parameters in terms of the moments and autocorrelations of observed underlying processes. Under moderate assumptions, which are typically much weaker than those for likelihood methods, we prove large-sample behaviors for our proposed estimators, including strong consistency and asymptotic normality. Our estimators obtain the canonical square-root convergence rate and are shown through numerical experiments to outperform likelihood-based methods.

A Strong Baseline and Batch Normalization Neck for Deep Person Re-Identification

This study explores a simple but strong baseline for person re-identification (ReID). Person ReID with deep neural networks has progressed and achieved high performance in recent years. However, many state-of-the-art methods design complex network structures and concatenate multi-branch features. In the literature, some effective training tricks briefly appear in several papers or source codes. The present study collects and evaluates these effective training tricks in person ReID. By combining these tricks, the model achieves 94.5% rank-1 and 85.9% mean average precision on Market1501 with only using the global features of ResNet50. The performance surpasses all existing global- and part-based baselines in person ReID. We propose a novel neck structure named as batch normalization neck (BNNeck). BNNeck adds a batch normalization layer after global pooling layer to separate metric and classification losses into two different feature spaces because we observe they are inconsistent in one embedding space. Extended experiments show that BNNeck can boost the baseline, and our baseline can improve the performance of existing state-of-the-art methods. Our codes and models are available at: https://github.com/michuanhaohao/reid-strong-baseline.

Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects

We consider a general class of observation-driven models with exogenous regressors for double bounded data that are based on the beta distribution. We obtain a stationary and ergodic beta observation-driven process subject to a contraction condition on the stochastic dynamic model equation. We derive conditions for strong consistency and asymptotic normality of the maximum likelihood estimator. The general results are used to study the properties of a beta autoregressive process with threshold effects and to establish the asymptotic properties of the maximum likelihood estimator. We employ the threshold autoregressive model with leverage effects to analyze realized correlations for several sets of stock returns. We find that the impact of past values of realized correlation on future values is at least 10% higher when stock returns are negative rather than positive. This finding supports the conjecture that correlation between stock returns tends to be higher when stock prices are falling, and lower when there is a surge in stock prices. Finally, we conduct an out-of-sample study that shows that our model with leverage effects can enhance the accuracy of point and density forecasts of realized correlations.

A nonparametric method of estimation of the population size in capture-recapture experiments.

A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf ( -class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed anddiscussed.

Strong consistency and asymptotic normality for quantities related to the Benjamini–Hochberg false discovery rate procedure

The Benjamini–Hochberg (BH) false discovery rate (FDR) procedure enjoys widespread use in multiple testing scenarios when the cost of false positives is low and the number of simultaneous tests prohibits use of the Bonferroni procedure. The FDR and the average power are each expected values, of the false discovery proportion (FDP) and true positive proportion (TPP), respectively. Chi (2007), proved a law of the iterated logarithm (LIL) for the positive proportion (PP), FDP and TPP, and discusses a criticality phenomenon whereby a minimal FDR corresponding to the effect size is required for a nonzero rate of positive calls. While almost sure convergence follows as a corollary, no direct simple proof exists in the literature. We provide this result under the same set of conditions. Of greater consequence, we prove central limit results (CLT) for the PP, FPF and TPP under these weak conditions, providing full characterization of the limits.

Estimation of causal continuous‐time autoregressive moving average random fields

AbstractWe estimate model parameters of Lévy‐driven causal continuous‐time autoregressive moving average random fields by fitting the empirical variogram to the theoretical counterpart using a weighted least squares (WLS) approach. Subsequent to deriving asymptotic results for the variogram estimator, we show strong consistency and asymptotic normality of the parameter estimator. Furthermore, we conduct a simulation study to assess the quality of the WLS estimator for finite samples. For the simulation, we utilize numerical approximation schemes based on truncation and discretization of stochastic integrals and we analyze the associated simulation errors in detail. Finally, we apply our results to real data of the cosmic microwave background.

Normalization proofs for the un-typed <i>μμ</i>'-calculus

A long-standing open problem of Parigot has been solved by David and Nour, namely, they gave a syntactical and arithmetical proof of the strong normalization of the untyped μμ'-reduction. In connection with this, we present in this paper a proof of the weak normalization of the μ and μ'-rules. The algorithm works by induction on the complexity of the term. Our algorithm does not necessarily give a unique normal form: sometimes we may get different normal forms depending on our choice. We also give a simpler proof of the strong normalization of the same reduction. Our proof is based on a notion of a norm defined on the terms.

Abstracting models of strong normalization for classical calculi

Modern programming languages have effects and mix multiple calling conventions, and their core calculi should too. We characterize calling conventions by their “substitution discipline” that says what variables stand for, and design calculi for mixing disciplines in a single program. Building on variations of the reducibility candidates method, including biorthogonality and symmetric candidates which are both specialized for one discipline, we develop a single uniform framework for strong normalization encompassing call-by-name, call-by-value, call-by-need, call-by-push-value, non-deterministic disciplines, and any others satisfying some simple criteria. We explicate commonalities of previous methods and show they are special cases of the uniform framework and they extend to multi-discipline programs.