Empirical Parameter Estimation Research Articles

Empirical likelihood and estimation in a partially linear varying coefficient model with right censored data

In this paper, we study the empirical likelihood and estimation of parameters of interest in a partially linear varying coefficient model with right censored data. Two cases are considered: censoring is independent of the covariates, and censoring depends on the covariates. The bias-corrected empirical log-likelihood ratios for the regression parameters are presented, Wilks' theorem is proved, and thus the confidence regions of the regression parameters are constructed. The estimators of parametric and nonparametric components are constructed, their asymptotic distributions are obtained, and the consistent estimators of the asymptotic variances are also given. Furthermore, the partial profile empirical log-likelihood ratios for each component of the regression parameters and the coefficient functions are constructed, and show they are asymptotically chi-squared. The obtained results can be directly used to construct the confidence regions/intervals for the regression parameters and the pointwise confidence intervals for the coefficient functions. Our approach is to directly calibrate the empirical log-likelihood ratio so that the resulting ratio is asymptotically chi-squared, undersmoothing of the coefficient functions is avoided, and existing data-driven methods can be effectively used to select the optimal bandwidth. Simulation studies compare the empirical likelihood method with one based on normal approximation and perform real data analysis.

Coupled data assimilation in climate research: A brief review of applications in ocean and land

Regions of the cryosphere, including the poles, that are currently unmonitored are expanding, therefore increasing the importance of satellite observations for such regions. With the increasing availability of satellite data in recent years, data assimilation research that combines forecasting models with observational data has begun to flourish. Coupled land/ice-atmosphere/ocean models generally improve the forecasting ability of models. Data assimilation plays an important role in such coupled models, by providing initial conditions and/or empirical parameter estimation. Coupled data assimilation can generally be divided into three types: uncoupled, weakly coupled, or strongly coupled. This review provides an overview of coupled data assimilation, introduces examples of its use in research on sea ice-ocean interactions and the land, and discusses its future outlook. Assimilation of coupled data constitutes an effective method for monitoring cold regions for which observational data are scarce and should prove useful for climate change research and the design of efficient monitoring networks in the future.

Traveling Wave-Based Fault Localization in FACTS-Compensated Transmission Line via Signal Decomposition Techniques

Modern power systems are structurally complex and are vulnerable to undesirable events like faults. In the event of faults in transmission line, accurate fault location improves restoration process, thereby enhancing the reliability of the overall system. Fault location methods (FLMs) are tools which assist in identifying fault locations quickly. However, the accuracy of these FLMs gets affected in the presence of flexible alternating current transmission system (FACTS) devices. Therefore, in this work, the performance of four different signal decomposition techniques aided traveling wave aided FLMs are qualitatively compared in the context of fault localization in FACTS-compensated systems. FLMs based on intrinsic time decomposition (ITD), empirical mode decomposition (EMD), S-transform (ST), and estimation of signal parameters via rotational invariance technique (ESPRIT) are investigated. The accuracy of FLMs is tested for different cases of series, shunt, and series-shunt FACTS-compensated systems. A 500 kV system employed with 100 MVAr FACTS device is used for simulation. The instant of arrival wave at end of transmission line is from all aforementioned FLMs. The obtained ATWs are used in fault localization. Further, the associated percentage errors are calculated. The results suggest that EMD and ESPRIT-based FLMs are more accurate than others.

The maximum likelihood ensemble smoother for the Kuramoto–Sivashinsky equation

AbstractData assimilation (DA) aims to combine observations/data with a model to maximize the utility of information for obtaining the optimal estimate. The maximum likelihood ensemble filter (MLEF) is a sequential DA method or a filter-type method. Weaknesses of the filter method are assimilating time-integrated observations and estimating empirical parameter estimation. The reason is that the forward model is employed outside of the analysis procedure in this type of DA method. To overcome these weaknesses, the MLEF is now extended as a smoother and the novel maximum likelihood ensemble smoother (MLES) is proposed. The MLES is a smoothing method with variational-like qualities, specifically in the cost function. Rather than using the error information from a single temporal location to solve for the optimal analysis update as done by the MLEF, the MLES can include observations and the forward model within a chosen time window. The newly proposed DA method is first validated by a series of rigorous and thorough performance tests using the Lorenz 96 model. Then, as DA is known to be used extensively to increase the predictability of the commonly chaotic dynamical systems seen in meteorological applications, this study demonstrates the MLES with a model chaotic problem governed by the 1D Kuramoto–Sivashinky (KS) equation. Additionally, the MLES is shown to be an effective method in improving the estimate of uncertain empirical model parameters. The MLES and MLEF are then directly compared and it is shown that the performance of the MLES is adequate and that it is a good candidate for increasing the predictability of a chaotic dynamical system. Future work will focus on an extensive application of the MLES to highly turbulent flows.

The Influence of Exchange Rate and Foreign Capital on the Performance of Inflation Targeting Framework in Indonesia

This study provides empirical evidence on the problem of the trilemma of monetary policy in an open economy, in the context of the effect of exchange rates and foreign capital flows on the performance of the ITF in Indonesia. The method used as an empirical estimate is the Structural Vector Autoregressive (SVAR) model. This model allows to include restrictions in the empirical estimation of parameters that measure the contemporaneous effect of one variable on another variable according to the structure of the macroeconomic model. Meanwhile, the lagged effects are estimated according to the VAR model. Therefore, the SVAR model is considered more appropriate than the ordinary VAR model because it can measure both the instantaneous effect and the intertemporal effect of the problem under study. The SVAR model uses restrictions that are consistent with the theoretical model in its estimation, regardless of the time-to-time effect of one variable on another. There are 9 variables in the SVAR model, namely: global risk, oil prices, federal funds rate, economic growth, inflation, interest rates, monetary policy, credit interest rates, foreign portfolio investment flows, and the rupiah exchange rate. All data used were obtained from several sources, including: Bank Indonesia, Central Statistics Agency, and IMF. Based on the estimation results, the exchange rate and foreign capital flows have a significant effect on inflation and economic growth, thus affecting the performance of the ITF in Indonesia. In particular, there is a relative influence between external factors, particularly global commodity prices, US monetary policy interest rates, and global risks, and domestic factors, particularly economic growth, monetary policy interest rates, and bank interest or credit rates. This study also concludes that in addition to inflation and economic growth considerations, Bank Indonesia also considers exchange rate movements in determining its interest rate policy response.

Entropy Tucker model: Mining latent mobility patterns with simultaneous estimation of travel impedance parameters

With the rapid increase in the availability of passive data in the field of transportation, combining machine learning with transportation models has emerged as an important research topic in recent years. This study proposes an entropy Tucker model that integrates (1) a Tucker decomposition technique, i.e., an existing machine learning method, and (2) an entropy maximizing model, i.e., an existing model used for modeling trip distribution in the field of transportation. In addition, an optimization algorithm is presented to empirically identify the proposed model. The proposed model provides a solid theoretical foundation for the machine learning method, substantially improves prediction performance, and provides richer behavioral implications through empirical parameter estimation of travel impedance. We conducted a case study using public transit smart card data. The results showed that the proposed model improves the prediction performance and interpretability of the results compared to the conventional nonnegative Tucker decomposition technique. Further, we empirically confirmed that the travel impedance varies with the origin–destination pair, time of the day, and day of the week. Finally, we discussed how embedding the theoretical foundations of transport modeling into machine learning methods can facilitate the use of various passive data in wider practical contexts of transport policy decision making.

A model of income evaluation: income comparison on subjective reference income distribution

ABSTRACT People’s evaluation of the relative position of their income is not as accurate as the relative income hypothesis assumes. It is observed from empirical survey data that income evaluation is concentrated in the middle. We develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. We conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. The theoretical analysis shows that the centralization of income evaluation distribution occurs when the subjective reference distribution is more dispersed than the objective distribution. Empirical analysis using Japanese data from 2015 shows that the relationship between subjective and objective distributions differed depending on social categories with different social experiences. Women had a more ambiguous distribution than men. Among men, those aged 45–54 had a subjective distribution closest to the objective distribution. Thus, the subjective reference income distributions that potentially define people’s evaluation of their income and their differences based on social category were only clarified by constructing the model.

Empirical method evaluation of charge – Changing cross sections

A method based on experimental data, theoretical models, and the empirical estimation of experimental parameters in the equilibrium charge distribution of ions is proposed to evaluate charge changing cross sections. This method makes it possible to obtain cross sections for loss and capture of one or several electrons in gaseous and solid targets with the inclusion of the influence of excited states of ions and target atoms.

The high-frequency response correction of eddy covariance fluxes – Part 2: An experimental approach for analysing noisy measurements of small fluxes

Abstract. Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem–atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical or experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by Ibrom et al. (2007a) (PSAI07), in which the noise and H are fitted in different frequency ranges, and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA21). For CSA, we use a method utilizing the square root of the H with shifted vertical wind velocity time series via cross-covariance maximization (CSAH,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA21 and CSAH,sync successfully estimate the expected time constant regardless of the degree of attenuation and SNR. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias between 0.1 % and 1.4 %. PSAA21 showed almost no bias, while CSAH,sync showed bias of ±0.4 %. The accuracies of both PSA and CSA methods were not significantly affected by SNR level, instilling confidence in EC flux measurements and data processing in set-ups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA21 outperforms PSAI07, while when using cospectra the CSAH,sync approach provides accurate results. These findings are independent of the SNR value and attenuation level.

A novel de‐noising method based on coherence average for ultrasonic signal of partial discharge in transformer

Ultrasonic method is widely used for the detection and location of partial discharge (PD) in transformer, however, the measured ultrasonic signal is usually corrupted by noise, and sometimes is even buried by noise entirely. Therefore, the de-noising of the measured signal is essential. Conventional de-nosing methods, such as wavelet method and singular value decomposition (SVD) method, generally require empirical parameter selection or estimation, and the best parameters for de-noising vary with the PD source and noise condition, which will bring some limitation to their applicability. More importantly, conventional de-noising methods usually have poor performance for the low signal-to-noise-ratio (SNR) signals. To improve this problem, the paper proposes a de-noising method based on coherence average for the ultrasonic signal. The de-noising performance of the proposed method is evaluated based on a comparison with conventional methods, the results indicate that the proposed method has great de-noising effect for the ultrasonic signals, even for the low-SNR signals. Besides, the proposed method is free from empirical parameter selection or estimation, which can make its applicability more extensive. The proposed method can offer a practical and effective solution to the de-noising of ultrasonic signal of PD in transformer.

Response time models separate single- and dual-process accounts of memory-based decisions

Human decisions often deviate from economic rationality and are influenced by cognitive biases. One such bias is the memory bias according to which people prefer choice options they have a better memory of—even when the options’ utilities are comparatively low. Although this phenomenon is well supported empirically, its cognitive foundation remains elusive. Here we test two conceivable computational accounts of the memory bias against each other. On the one hand, a single-process account explains the memory bias by assuming a single biased evidence-accumulation process in favor of remembered options. On the contrary, a dual-process account posits that some decisions are driven by a purely memory-driven process and others by a utility-maximizing one. We show that both accounts are indistinguishable based on choices alone as they make similar predictions with respect to the memory bias. However, they make qualitatively different predictions about response times. We tested the qualitative and quantitative predictions of both accounts on behavioral data from a memory-based decision-making task. Our results show that a single-process account provides a better account of the data, both qualitatively and quantitatively. In addition to deepening our understanding of memory-based decision-making, our study provides an example of how to rigorously compare single- versus dual-process models using empirical data and hierarchical Bayesian parameter estimation methods.

A Neuron-Based Kalman Filter with Nonlinear Autoregressive Model.

The control effect of various intelligent terminals is affected by the data sensing precision. The filtering method has been the typical soft computing method used to promote the sensing level. Due to the difficult recognition of the practical system and the empirical parameter estimation in the traditional Kalman filter, a neuron-based Kalman filter was proposed in the paper. Firstly, the framework of the improved Kalman filter was designed, in which the neuro units were introduced. Secondly, the functions of the neuro units were excavated with the nonlinear autoregressive model. The neuro units optimized the filtering process to reduce the effect of the unpractical system model and hypothetical parameters. Thirdly, the adaptive filtering algorithm was proposed based on the new Kalman filter. Finally, the filter was verified with the simulation signals and practical measurements. The results proved that the filter was effective in noise elimination within the soft computing solution.

Rain attenuation and worst month statistics verification and modeling for 5G radio link system at 26 GHz in Malaysia

AbstractThe explosive daily dependence on wireless communication services necessitates the research to establish ultrawideband communication systems with ultrahigh bit rate transmission capabilities. The advent of the fifth‐generation (5G) microwave link transmitting at millimeter‐wave (mm‐wave) frequency band is a promising technology to accommodate the escalating demand for wireless services. In this frequency band, however, the behavior of the transmission channel and its climatic properties are a major concern. This is of particular importance in tropical regions where the climate is mainly rainy with large raindrop size and high rainfall rate that may interact destructively with the propagating signal and cause total attenuation for the signal. International Telecommunication Union (ITU) introduced a global rain attenuation model to characterize the effect of rain on the propagating signal at a wideband of frequencies. The validity of this model in tropical regions is still an open question for research. In this paper, real measurements are conducted at Universiti Teknologi Malaysia (UTM), Johor Bahru, Malaysia, to investigate the impact of rain on the propagation of mm‐waves at 26 GHz over the microwave 5G radio link system. Rainfall rate and rain attenuation data sets are collected for one year at one sample per min sampling rate. Both data sets are used to estimate signal propagation conditions in comparison to the ITU model prediction. From the presented results, it is found that at 0.01% percentage of time and rainfall rate of about 120 mm/hr, the propagated signal would experience 26.2 dB losses per kilometer traveled. In addition, there is a significant deviation between the empirical estimation of the worst month parameters and the ITU worst month parameter prediction. Similarly, rainfall rate and rain attenuation estimated through the ITU model imposes a large deviation as compared with the measurements. Furthermore, more accurate empirical worst month parameters are proposed that yielded more accurate estimation of the worst month rainfall and rain attenuation predictions in comparison to the ITU model predictions.

Estimation of Random Coefficient Multilevel Models in the Context of Small Numbers of Level 2 Clusters.

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the treatment of multilevel data specifically when there is random coefficient variation in small samples. The methods being compared are fixed effects modeling (the industry standard in business and managerial sciences), multilevel modeling using restricted maximum likelihood (REML) estimation (the industry standard in the social and behavioral sciences), multilevel modeling using the Kenward-Rogers correction, and Bayesian estimation using Markov Chain Monte Carlo. Results indicate that multilevel modeling does have an advantage over fixed effects modeling when Level 2 slope parameter variance exists. Bayesian estimation of multilevel effects can be advantageous over traditional multilevel modeling using REML, but only when prior probabilities are correctly specified. Results are presented in terms of Type I error, power, parameter estimation bias, empirical parameter estimate standard error, and parameter 95% coverage rates, and recommendations are presented.

Boundary Crossing Probabilities for General Exponential Families

We consider parametric exponential families of dimension K on the real line. We study a variant of boundary crossing probabilities coming from the multi-armed bandit literature, in the case when the real-valued distributions form an exponential family of dimension K. Formally, our result is a concentration inequality that bounds the probability that B ψ (θ n , θ*) ≥ f(t/n)/n, where θ* is the parameter of an unknown target distribution, θ n is the empirical parameter estimate built from n observations, ψ is the log-partition function of the exponential family and B ψ is the corresponding Bregman divergence. From the perspective of stochastic multi-armed bandits, we pay special attention to the case when the boundary function f is logarithmic, as it is enables to analyze the regret of the state-of-the-art KL-ucb and KL-ucb+ strategies, whose analysis was left open in such generality. Indeed, previous results only hold for the case when K = 1, while we provide results for arbitrary finite dimension K, thus considerably extending the existing results. Perhaps surprisingly, we highlight that the proof techniques to achieve these strong results already existed three decades ago in the work of T. L. Lai, and were apparently forgotten in the bandit community. We provide a modern rewriting of these beautiful techniques that we believe are useful beyond the application to stochastic multi-armed bandits.

Savings Adequacy Assessment: The Case of Malaysian Employees Provident Fund Members

This study examines the potential consequences of early withdrawals from the Malaysian Employees Provident Fund in patterns of savings adequacy by studying the impact of house purchase on household lifecycle consumption. The authors develop an overlapping generations model of a small open economy where investment is available to capital, housing, and financial instruments. Housing is modelled as an asset subject of transaction costs. In equilibrium setting, the empirical estimation of exogenous system parameters sets the optimal levels of consumption and savings. The authors perform empirical analysis by taking into consideration four different scenarios: different employment periods (18-55 vs. 25-55), different retirement periods (55-65 vs. 55-75 vs. 55-85), housing vs. non-housing consumption, and theoretical vs actual contribution rates. Actuarial evaluation shows that low-income employees can have sufficient income to meet their retirement needs in the absence of housing consumption. Policy directions are also discussed.

지형학적 인자에 따라 군집화된 중소규모유역의 합성단위도법 제시

유역의 지형학적특성을 이용한 합성단위도법을 제시하였다. 합성단위도 산정을 위하여 19개 유역에 대하여 6개 지형학적 인자를 사용하였으며, 전체유역을 유역면적 <TEX>$ 200km^2$</TEX>을 기준으로 2개의 군집으로 분류하였다. 19개 유역을 대상으로 군집별로 표준화된 지형학적 인자와 유역별 대표단위도의 첨두비유량 및 첨두시간과의 회귀식을 제시하였으며, Nash와 Clark 단위도를 유도하였다. 합성단위도의 모의정확도 검증을 위해 추가적으로 선택한 6개 유역에서 2010-2011년에 발생한 145개 강우-유출사상에 적용하여 경험식을 사용한 Clark모형의 적용결과와 비교하였다. 검증결과 기존의 합성단위도법에 비해 높은 정확도를 나타내었으며, 이러한 결과는 미계측 유역에서의 적용 가능성을 보여주었다. The methodology of synthetic unit hydrograph using geomorphic characteristics was suggested. Six geomorphic components over 19 watersheds were used to estimate synthetic unit hydrograph and the test watersheds were classified into two groups on the basis of the area of <TEX>$200km^2$</TEX>. The regression formulas between standardized geomorphic characteristics for each group and peak quantities of specific streamflow and time of representative unit hydrograph were suggested and the Nash and the Clark unit hydrographs were derived. For verifying the derived unit hydrographs, the resulting hydrographs were compared with the ones using the existing Clark unit hydrographs based on the empirical parameter estimation for the 145 storm events during 2010 to 2011 for the additional six watersheds. The results showed the relatively higher performance over the existing synthetic unit hydrograph methods, which could be a contribution to the hydrologic estimation in ungauged watersheds.

A nonstationary bias‐correction technique to remove bias in GCM simulations

AbstractWe developed an updated nonstationary bias‐correction method for a monthly global climate model of temperature and precipitation. The proposed method combines two widely used quantile mapping bias‐correction methods to eliminate potential illogical values of the variable. Instead of empirical parameter estimation in the more‐common quantile mapping method, our study compared bias‐correction performance when parametric or nonparametric procedures were used to estimate the probability distribution. The results showed our proposed bias‐correction method to be very effective in reducing the model bias: it removed over 80% and 83% of model bias for surface air temperature and precipitation, respectively, during the validation period. Compared with a widely used method of bias correction (delta change), our proposed technique demonstrates improved correction of the distribution of variables. In addition, nonparametric estimation procedures further reduced the mean absolute errors in temperature and precipitation during the validation period by approximately 2% and 0.4%, respectively, compared with parametric procedures. The proposed method can remove over 40% and 60% of the uncertainty from model temperature and precipitation projections, respectively, at the global land scale.

Latent dirichlet allocation

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

Empirical Bayes estimation of parameters in Markov transition probability matrix with computational methods

Empirical Bayes estimator for the transition probability matrix is worked out in the cases where we have belief regarding the parameters, For example, where the states seem to be equal or not. In both cases, priors are in accordance with our beliefs. Using EM algorithm, computational methods for different hyperparameters of the empirical Bayes are described. Also, robustness of empirical Bayes procedure is investigated.