亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We introduce a procedure for conditional density estimation under logarithmic loss, which we call SMP (Sample Minmax Predictor). This estimator minimizes a new general excess risk bound for statistical learning. On standard examples, this bound scales as $d/n$ with $d$ the model dimension and $n$ the sample size, and critically remains valid under model misspecification. Being an improper (out-of-model) procedure, SMP improves over within-model estimators such as the maximum likelihood estimator, whose excess risk degrades under misspecification. Compared to approaches reducing to the sequential problem, our bounds remove suboptimal $\log n$ factors and can handle unbounded classes. For the Gaussian linear model, the predictions and risk bound of SMP are governed by leverage scores of covariates, nearly matching the optimal risk in the well-specified case without conditions on the noise variance or approximation error of the linear model. For logistic regression, SMP provides a non-Bayesian approach to calibration of probabilistic predictions relying on virtual samples, and can be computed by solving two logistic regressions. It achieves a non-asymptotic excess risk of $O((d + B^2R^2)/n)$, where $R$ bounds the norm of features and $B$ that of the comparison parameter; by contrast, no within-model estimator can achieve better rate than $\min({B R}/{\sqrt{n}}, {d e^{BR}}/{n} )$ in general. This provides a more practical alternative to Bayesian approaches, which require approximate posterior sampling, thereby partly addressing a question raised by Foster et al. (2018).

This paper focuses on obtaining a posteriori error estimates for mixed-dimensional elliptic equations exhibiting a hierarchical structure. We derive general abstract estimates based on the theory of functional a posteriori error estimates, for which guaranteed upper bounds for the primal and dual variables and two-sided bounds for the primal-dual pair are obtained. However, unlike standard results obtained with the functional approach, we propose four different ways of estimating the residual errors based on the level of accuracy available for their approximations, i.e.: (1) no conservation, (2) subdomain conservation, (3) local conservation, and (4) exact conservation. This treatment results in sharper and fully computable estimates when mass is conserved either locally or exactly, with a comparable structure to those obtained from grid-based a posteriori techniques. We demonstrate the practical effectiveness of our theoretical results through numerical experiments using four different discretization methods on matching and nonmatching grids for synthetic problems and benchmarks of flow in fractured porous media.

This paper provides some extended results on estimating the parameter matrix of high-dimensional regression model when the covariate or response possess weaker moment condition. We investigate the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266, 2021) for matrix completion model with $(1+\epsilon)$-th moments. The corresponding phase transition phenomenon is observed. When $\epsilon \geq 1$, the robust estimator possesses the same convergence rate as previous literature. While $1> \epsilon>0$, the rate will be slower. For high dimensional multiple index coefficient model, we also apply the element-wise truncation method to construct a robust estimator which handle missing and heavy-tailed data with finite fourth moment.

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate this inverse problem as minimizing a local patch-based cost function and use total derivative to approximate the gradient which is used in gradient descent to solve the problem. We analyze factors affecting the convergence and quality of the output in the Fourier domain. We also study the application of accelerated gradient descent algorithms in three gradient-free reverse filters, including the one proposed in this paper. We present results from extensive experiments to evaluate the complexity and effectiveness of the proposed algorithm. Results demonstrate that the proposed algorithm outperforms the state-of-the-art in that (1) it is at the same level of complexity as that of the fastest reverse filter, but it can reverse a larger number of filters, and (2) it can reverse the same list of filters as that of the very complex reverse filter, but its complexity is much smaller.

This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow for autoregressive dynamics in the observable process, Markov regime sequences with covariate-dependent transition matrices, and possible model misspecification. A Monte Carlo study examines the finite-sample properties of the ML estimator in correctly specified and misspecified models. An empirical application is also discussed.

The use of Bayesian filtering has been widely used in mathematical finance, primarily in Stochastic Volatility models. They help in estimating unobserved latent variables from observed market data. This field saw huge developments in recent years, because of the increased computational power and increased research in the model parameter estimation and implied volatility theory. In this paper, we design a novel method to estimate underlying states (volatility and risk) from option prices using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), further using it for option price prediction. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state estimation of Black-Scholes model under a GARCH model dynamics. We employ an Average and Best case switching strategy for adaptive state estimation of a non-linear, discrete-time state space model (SSM) like Black-Scholes, using PCRLB based performance measure to judge the best filter at each time step [1]. Since estimating closed-form solution of PCRLB is non-trivial, we employ a particle filter based approximation of PCRLB based on [2]. We test our proposed framework on option data from S$\&$P 500, estimating the underlying state from the real option price, and using it to estimate theoretical price of the option and forecasting future prices. Our proposed method performs much better than the individual applied filter used for estimating the underlying state and substantially improve forecasting capabilities.

Unlike univariate extreme value theory, multivariate extreme value distributions cannot be specified through a finite-dimensional parameter family of distributions. Instead, the many facets of multivariate extremes are mirrored in the inherent dependence structure of component-wise maxima which must be dissociated from the limiting extreme behaviour of its marginal distribution functions before a probabilistic characterisation of an extreme value quality can be determined. Mechanisms applied to elicit extremal dependence typically rely on standardisation of the unknown marginal distribution functions from which pseudo-observations for either Pareto or Fr\'echet marginals result. The relative merits of both of these choices for transformation of marginals have been discussed in the literature, particularly in the context of domains of attraction of an extreme value distribution. This paper is set within this context of modelling penultimate dependence as it proposes a unifying class of estimators for the residual dependence index that eschews consideration of choice of marginals. In addition, a reduced bias variant of the new class of estimators is introduced and their asymptotic properties are developed. The pivotal role of the unifying marginal transform in effectively removing bias is borne by a comprehensive simulation study. The leading application in this paper comprises an analysis of asymptotic independence between rainfall occurrences originating from monsoon-related events at several locations in Ghana.

This paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We regard the joint as a single complex parameter and derive a new form of the likelihood equation of a complex variable. Based on the equation, we provide a new iterative scheme approximating the maximum likelihood estimate. We also handle the equation in an algebraic manner and derive a polynomial containing the maximum likelihood estimate as a root. This algebraic approach provides another scheme approximating the maximum likelihood estimate by root-finding algorithms for polynomials, and furthermore, gives non-existence of closed-form formulae for the case that the sample size is five. We finally provide some numerical examples to show our method is effective.

For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite element method (FEM). In solving the optimization problem corresponding to the interpolation error constant, the maximum norm in the constraint condition is the most difficult part to process. To handle this difficulty, a novel method is proposed by combining the orthogonality of the interpolation associated to the Fujino--Morley FEM space and the convex-hull property of the Bernstein representation of functions in the FEM space. Numerical results for the lower and upper bounds of the interpolation error constant for triangles of various types are presented to verify the efficiency of the proposed method.

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.