Search Results (34)

This study includes a comprehensive evaluation of six penalty estimation strategies for partially linear models (PLRMs), focusing on their performance in the presence of multicollinearity and their ability to handle both parametric and nonparametric components. The methods under consideration include Ridge regression, Lasso, Adaptive Lasso (aLasso), smoothly clipped absolute deviation (SCAD), ElasticNet, and minimax concave penalty (MCP). In addition to these established methods, we also incorporate Stein-type shrinkage estimation techniques that are standard and positive shrinkage and assess their effectiveness in this context. To estimate the PLRMs, we consider a kernel smoothing technique grounded in penalized least squares. Our investigation involves a theoretical analysis of the estimators’ asymptotic properties and a detailed simulation study designed to compare their performance under a variety of conditions, including different sample sizes, numbers of predictors, and levels of multicollinearity. The simulation results reveal that aLasso and shrinkage estimators, particularly the positive shrinkage estimator, consistently outperform the other methods in terms of Mean Squared Error (MSE) relative efficiencies (RE), especially when the sample size is small and multicollinearity is high. Furthermore, we present a real data analysis using the Hitters dataset to demonstrate the applicability of these methods in a practical setting. The results of the real data analysis align with the simulation findings, highlighting the superior predictive accuracy of aLasso and the shrinkage estimators in the presence of multicollinearity. The findings of this study offer valuable insights into the strengths and limitations of these penalty and shrinkage strategies, guiding their application in future research and practice involving semiparametric regression. Full article

Introduced as a complementary concept to Shannon entropy, extropy provides an alternative perspective for measuring uncertainty. While useful in areas such as reliability theory and scoring rules, extropy in its original form treats all outcomes equally, which can limit its applicability in real-world settings where different outcomes have varying degrees of importance. To address this, the weighted extropy measure incorporates a weight function that reflects the relative significance of outcomes, thereby increasing the flexibility and sensitivity of uncertainty quantification. In this paper, we propose a novel recursive non-parametric kernel estimator for weighted extropy based on $\alpha$-mixing dependent observations, a common setting in time series and stochastic processes. The recursive formulation allows for efficient updating with sequential data, making it particularly suitable for real-time analysis. We establish several theoretical properties of the estimator, including its recursive structure, consistency, and asymptotic behavior under mild regularity conditions. A comprehensive simulation study and data application demonstrate the practical performance of the estimator and validate its superiority over the non-recursive kernel estimator in terms of accuracy and computational efficiency. The results confirm the relevance of the method for dynamic, dependent, and weighted systems. Full article

In many real-world situations, we deal with data that exhibit both randomness and vagueness. To manage such uncertain information, fuzzy theory provides a useful framework. Specifically, to explore causal relationships in these datasets, a lot of fuzzy regression models have been introduced. However, while fuzzy regression analysis focuses on estimation, it is equally important to study the mathematical characteristics of fuzzy regression estimates. Despite the statistical significance of optimal properties in large-sample scenarios, only limited research has addressed these topics. This study establishes key optimal properties, such as strong consistency and asymptotic normality, for the fuzzy least-squares estimator (FLSE) in general linear regression models involving fuzzy input–output data and random errors. To achieve this, fuzzy analogues of traditional normal equations and FLSEs are derived using a suitable fuzzy metric. Additionally, a confidence region based on FLSEs is proposed to facilitate inference. The asymptotic relative efficiency of FLSEs, compared to conventional least-squares estimators, is also analyzed to highlight the efficiency of the proposed estimators. Full article

In cryptography, techniques and tools developed in the subfield of linear cryptanalysis have previously successfully been used to allow attackers to break many sophisticated cryptographic ciphers. Since these linear cryptanalytic techniques require exploitable linear approximations to relate the input and output of vectorial Boolean functions, e.g., the plaintext, ciphertext, and key of the cryptographic function, finding these approximations is essential. For this purpose, the Correlation Extraction Algorithm (CEA), which leverages the emerging field of quantum computing, appears promising. However, there has been no comprehensive analysis of the CEA regarding finding an exploitable linear approximation for linear cryptanalysis. In this paper, we conduct a thorough theoretical analysis of the CEA. We aim to investigate its potential in finding a linear approximation with prescribed statistical characteristics. To support our theoretical work, we also present the results of a small empirical study based on a computer simulation. The analysis in this paper shows that an approach that uses the CEA to find exploitable linear approximations has an asymptotic advantage, reducing a linear factor to a logarithmic one in terms of time complexity, and an exponential advantage in terms of space complexity compared to a classical approach that uses the fast Walsh transform. Furthermore, we show that in specific scenarios, CEA can exponentially reduce the search space for exploitable linear approximations in terms of the number of input bits of the cipher. Neglecting the unresolved issue of efficiently checking the property of linear approximations measured by the CEA, our results indicate that the CEA can support the linear cryptanalysis of vectorial Boolean functions with relatively few (e.g., $n\le 32$) output bits. Full article

Wavelet analysis algorithms in combination with thresholding procedures are widely used in nonparametric regression problems when estimating a signal function from noisy data. The advantages of these methods lie in their computational efficiency and the ability to adapt to the local features of the estimated function. It is usually assumed that the signal function belongs to some special class. For example, it can be piecewise continuous or piecewise differentiable and have a compact support. These assumptions, as a rule, allow the signal function to be economically represented on some specially selected basis in such a way that the useful signal is concentrated in a relatively small number of large absolute value expansion coefficients. Then, thresholding is performed to remove the noise coefficients. Typically, the noise distribution is assumed to be additive and Gaussian. This model is well studied in the literature, and various types of thresholding and parameter selection strategies adapted for specific applications have been proposed. The risk analysis of thresholding methods is an important practical task, since it makes it possible to assess the quality of both the methods themselves and the equipment used for processing. Most of the studies in this area investigate the asymptotic order of the theoretical risk. In practical situations, the theoretical risk cannot be calculated because it depends explicitly on the unobserved, noise-free signal. However, a statistical risk estimate constructed on the basis of the observed data can also be used to assess the quality of noise reduction methods. In this paper, a model of a signal contaminated with additive Gaussian noise is considered, and the general formulation of the thresholding problem with threshold functions belonging to a special class is discussed. Lower bounds are obtained for the threshold values that minimize the unbiased risk estimate. Conditions are also given under which this risk estimate is asymptotically normal and strongly consistent. The results of these studies can provide the basis for further research in the field of constructing confidence intervals and obtaining estimates of the convergence rate, which, in turn, will make it possible to obtain specific values of errors in signal processing for a wide range of thresholding methods. Full article

Efficiently quantifying stand density is crucial in sustainably managing mid-rotation loblolly pine (Pinus taeda L.) plantations. While various stand density measures, including basal area (BA), stand density index (SDI), relative spacing (RS), and live crown length ratio (CR), are used, ambiguity persists among these measures: are they each biologically sound and are they on par with each other in terms of density management? These topics were investigated by examining the relationships between measures and stand age, between measures and tree growth, and between measures using data from numerous long-term permanent plots established in loblolly pine plantations in east Texas. A strong trend of increasing density with age was found for all the measures. The trend followed an asymptotic trajectory when density was expressed as BA, SDI, or RS, adhering to biological expectations, but the trend showed a gradual decrease for CR. Strong and biologically sound relationships between DBH periodic annual increment (${\mathrm{P}\mathrm{A}\mathrm{I}}_{\mathrm{D}}$) and BA or SDI were observed, suggesting that both measures match true DBH growth. However, ${\mathrm{P}\mathrm{A}\mathrm{I}}_{\mathrm{D}}$ linearly decreased with decreasing RS and with decreasing CR in a smooth curve, biasing from the biological expectation. Strong relationships existed between the measures, suggesting that these seemingly disparate measures are not independent of each other. Site index affected all investigated relationships in a manner of having higher densities at a given age or a greater ${\mathrm{P}\mathrm{A}\mathrm{I}}_{\mathrm{D}}$ at a given density for higher site index sites regardless of measures. The effects of initial planting density on the relationships were mostly negligible, having no practical significance, with few exceptions (the relationships of SDI–age, RS–age, and CR–RS). Among the measures evaluated, our results advocate for the use of $\mathrm{B}\mathrm{A}$ to regulate mid-rotation loblolly pine plantation density such as determining the approximate biological timing for thinning in the Western Gulf region due to its biological soundness, ease of measurement, and feasibility of incorporating effects of site quality and planting density. Full article

The purpose of this paper is to discuss the problem of estimation and testing the equality of two autoregressive parameters of two first-order autoregressive processes $\mathit{AR}\left(1\right)$, where for each process, the observations are made at different time points. The primary interest is to propose the testing procedures for the homogeneity of autocorrelation parameters ${\rho }_1$ and ${\rho }_2$. Furthermore, we are interested in estimating ${\rho }_1$ under uncertain and weak prior information about the possible equality of ${\rho }_1$ and ${\rho }_2$, though we may not have full confidence in the tenacity of this information. A large sample test for the homogeneity of the parameters is developed. Pooled “P” (or restricted estimator) and preliminary test “PT” estimators are proposed, and their properties are investigated and compared with the unrestricted estimator “UE” of ${\rho }_1$. Full article

We consider authenticating multicast messages in the case of extremely narrow communication channels, such as underwater acoustic communication, with devices such as mobile sensors creating a self-organizing autonomous network. Channel characteristics in this scenario prevent the application of digital signatures (and asymmetric cryptography in general), as it would consume too much of the available bandwidth. As communication is relatively sparse, standard symmetric methods such as TESLA have limited application in this scenario as well. Driven by real-world requirements, we focus on tiny networks of only a few nodes. This paper discusses two issues: (a) strategies of key predistribution enabling flexible creation of multicast groups; (b) authenticating multicast messages in a way that prevents an attacker impersonating the sender by subverting one or more receiver nodes and learning the symmetric keys stored by these nodes. For tiny networks, we show that scalable and asymptotically efficient solutions might be useless, and that specially tailored combinatorial approaches may confer some advantage. Full article

In this study, we explore a downlink cellular network where each base station (BS) engages in simultaneous communication with multiple users through spatial division multiple access (SDMA). The positions of both BSs and users are established through independent random point processes, effectively representing the cellular network. SDMA utilizes block diagonalization (BD) at each BS, employing multiple receive antennas for each user. To implement BD, users quantize and provide feedback on their downlink channels to their respective BSs. The net spectral efficiency, measuring the effective rate accounting for both downlink and uplink resource usage, serves as a performance metric. In prior research, the optimal feedback rate in terms of maximizing net spectral efficiency has been approximated in this scenario. The corresponding approximations effectively illustrate the asymptotic behavior of the optimal number as a function of the length of the coherent channel block. However, the accuracy of the approximation diminishes when the length of the coherent channel block is relatively small. Given that the length of the coherent channel block can assume relatively small values depending on wireless environments, achieving a precise estimate across the entire range of the coherent block length holds significant importance. Consequently, this paper focuses primarily on enhancing the accuracy of the approximation for the optimal feedback rate. In order to achieve a more precise estimation, we analyze the derivative of the net spectral efficiency, which encompasses two functions that demonstrate distinct growth rates. In contrast to prior studies, both functions are rigorously approximated through mathematical analysis. As a result, the proposed approximation significantly improves the accuracy compared to previous studies, particularly when dealing with short coherent channel block lengths. Moreover, this approximation generally achieves near-optimal performance, regardless of system parameters. Full article

The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence. Full article

The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency ($ARE$) of the Kaplan–Meier survival estimator compared to parametric survival estimators. We begin by generalizing Miller’s approach and presenting a formula that enables the estimation (numerical or exact) of $ARE$ for various survival distributions and types of censoring. We examine the effect of follow-up time and censoring on $ARE$. The article concludes with a discussion about the reasons behind the lower and time-dependent $ARE$ of the Kaplan–Meier survival estimator. Full article

Probability life distributions usually describe the time to an event or survival time. Therefore, these life distributions play a crucial role in the analysis and projection of maximum life expectancy using the goodness of fit approach for nonparametric hypothesis testing. This study suggests a nonparametric technique to determine whether the data follow an exponential distribution or belong to the mathematical class of the moment generating function for used better than aged (UBAmgf). These tests can be applied to both censored and non-censored data. The upper percentile points of the test statistics are generated, and the suggested test’s asymptotic normality is established. Some well-known alternative asymmetric probability models are used to compute the Pitman asymptotic relative efficiency (PARE) and powers of the proposed test. To demonstrate the paper’s conclusions, some asymmetric real-world datasets are examined. Full article

The aim of this paper is to extract the maximum power from wind energy for the doubly fed induction generator based wind turbine system (DFIG-WT) under the continuous stochastic perturbations of wind speed. The DFIG-WT is modeled as the Itô stochastic differential equations. The stochastic backstepping control method and the gain suppressing inequality technique are employed to guarantee that the relative rotor speed to the optimal value is bounded in probability. Furthermore, we extend the bounded result to the asymptotic stability of the rotor speed control loop. In addition, the parametric uncertainties in DFIG-WT are also considered in our control synthesis. The simplicity, robustness and efficiency of the designed controller are verified under the special wind speed with white noise by the numerical simulation of a 660 KW DFIG-WT. Full article

The Receiver Operating Characteristic (ROC) is a de facto standard for determining the accuracy of in vitro diagnostic (IVD) medical devices, and thus the exactness in its probability distribution is crucial toward accurate statistical inference. We show the exact probability distribution of the ROC AUC-value, hence exact critical values and p-values are readily obtained. Because the exact calculations are computationally intense, we demonstrate a method of geometric interpolation, which is exact in a special case but generally an approximation, vastly increasing computational speeds. The method is illustrated through open access data, demonstrating superiority of 26 composite biomarkers relative to a predicate device. Especially under correction for testing of multiple hypotheses, traditional asymptotic approximations are encumbered by considerable imprecision, adversely affecting IVD device development. The ability to obtain exact p-values will allow more efficient IVD device development. Full article

This study, dedicated to flapping wing propulsion in immediate proximity to a wall or between closely spaced flat walls, makes use of the method of matched asymptotic expansions. Its purpose is to create a simplified parametric model of such a propulsion system based on a single major assumption: immediate closeness of oscillating wing to a solid wall. In the case of a rectangular finite-aspect ratio wing, analytical expressions have been obtained for the coefficients of instantaneous and period-averaged thrust force as well as for the efficiency of the propulsor as a function of distance from the wall, Strouhal number and wing aspect ratio for selected cases of heaving, pitching and combined oscillations. It is shown that for some oscillation modes closeness to the ground results in increases in thrust and efficiency, and that optimally combined (considering ratio of the amplitudes and phase shift of contributing motions) heave–pitch oscillations allow to maximize thrust or efficiency of the flapping-wing propulsor. Increase in aspect ratio and decrease in Strouhal number (relative frequency of oscillations) in the case of heaving invariably brings about the increase in the ideal efficiency. An example is provided of a non-planar extreme ground effect application considering oscillations of a ring-wing embracing circular cylinder. A rule is derived for recalculation of the characteristics of the flapping-wing propulsor near a flat wall onto the characteristics of the same wing operating in a narrow canal between parallel walls. This rule can also be applied to evaluate propulsive properties of a ring-wing oscillating between co-axial cylindric surfaces. Full article