Non-parametric generalised newsvendor model

The systematic risk estimation models: A different perspective

There is a long-standing debate in the statistical, epidemiological, and econometric fields as to whether nonparametric estimation that uses machine learning in model fitting confers any meaningful advantage over simpler, parametric approaches in finite sample estimation of causal effects. We address the question: when estimating the effect of a treatment on an outcome, how much does the choice of nonparametric vs parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach to compare estimators across a large number of data-generating mechanisms drawn from nonparametric models with semi-informative priors. We apply this proposed approach and compare the performance of two nonparametric estimators (Bayesian adaptive regression tree and a targeted minimum loss-based estimator) to two parametric estimators (a logistic regression-based plug-in estimator and a propensity score estimator) in terms of estimating the average treatment effect across thousands of data-generating mechanisms. We summarize performance in terms of bias, confidence interval coverage, and mean squared error. We find that the two nonparametric estimators can substantially reduce bias as compared to the two parametric estimators in large-sample settings characterized by interactions and nonlinearities while compromising very little in terms of performance even in simple, small-sample settings.

We consider the problem of choosing between two density estimates, a non-parametric estimate with the the standard properties of nonparametric estimates (universal consistency, robustness, but not extremely good rate of convergence) and a special estimate designed to perform well on a given set T of densities. The special estimate can often be thought of as a parametric estimate. The selection we propose is based upon the L1 distance oetween both estimates. Among otner things, we show how one should proceed to insure that the selected estimate matches the special estimate's rate on T, and that it matches the nonparametric estimate's rate off T

Uno de los principales objetivos del área de confiabilidad es estimar la función de confiabilidad, donde tradicionalmente se utilizan estimadores no paramétricos, que son más eficientes en tamaños de muestras considerables. En este trabajo se comparan los estimadores no paramétricos para la función de confiabilidad a través del error cuadrático medio, utilizando los estimadores no paramétricos de Kaplan y Meier (1958), el estimador de Nelson (1969) y Bootstrap aplicado a Kaplan y Meier y Nelson. La comparación se hace teniendo en cuenta las estimaciones paramétricas, mediante simulación con diferentes escenarios, tiempos de interés, tamaños de muestra y porcentajes de censura, y muestra que el remuestreo Bootstrap tipo normal no presenta los mejores resultados con Kaplan y Meier (1958). Y mediante Nelson (1969), el 18 % fue más eficiente.

In today’s competitive marketplace demand, evaluation and selection of suppliers are pivotal for firms, and therefore decision makers need to select suppliers and the optimal order quantities when outsourcing. However, there is uncertainty and risk due to lack of precise data for supplier selection. Uncertainty can impose shortage or overstocks, because of stochastic demand, to firms; in this case, considering inventory control is essential. In this research, an appropriate spatial model is developed for a multi-product supplier selection model with service level and budget constraints. Learning Vector Quantization Neural Network is used to find the optimal number of decision variables with the goal of maximizing the expected profit of supply chains. By analyzing a practical example and conducting sensitivity analysis, we find that corporate profit will be maximized if the optimal integration of suppliers and the optimal order quantities from each supplier is determined. In addition, budget and service level should be considered in the process of finding the best result.

In this thesis, we cope with the fundamental mathematical and physical problems of the space-time-Doppler UWB system design for fading channels: multi-input multi-output (MIMO) wireless communication with adaptive filtering. The estimation algorithm from equalizer providing an accurate parameters estimate is investigated. UWB radio is a fast emerging technology with uniquely attractively features inviting major advances in wireless communications, networking, radar, imaging, and positioning systems. By its rule-making proposal in 2002, the Federal Communications Commission (FCC) in the United States essentially unleashed huge new bandwidth (3.6-10.6 GHz) at the noise floor, where UWB radios overlaying coexistence RF systems cerate using low-power ultra-short information bearing pulses. Right now, there are three basic types of UWB: multiband OFDM UWB (MB-OFDM UWB), impulse-UWB (I-UWB), and direct sequence UWB (DS-UWB). We focus on I-UWB and MB-OFDM-UWB, and compare their performance. A simple means for spreading the spectrum of low duty cycle pulse trains is time hopping (TH), with pulse position modulation (PPM) for data modulation at the rate of many pulses per data bit. The main contribution of this thesis for I-UWB is the design of leading edge detectors, coherent correlation detector (CCD), and pilot performance enhancement compared with different Rayleigh and Ricean fading conditions. For MB-OFDM UWB, we have considered the performance analysis and design criteria of MIMO OFDM UWB systems for high data-rate wireless transmission. The signal processing of frame detection, time synchronization, frequency synchronization, channel estimation, synchronization tracking using pilot subcarriers and 2-D MIMO detection algorithms is discussed. The main contributions of this thesis are 1) Compared with receiver employing the Maximum Likelihood (ML) detector, the receiver employing a low-complexity linear Minimum Mean Square Error (MMSE) demodulator can perform a limited performance loss in spatially uncorrelated channels. 2) Due to the operations of spreading and dispreading combined with MMSE-based frequency domain equalization, the adverse effects of the low-SNR subcarriers on the average BER performance are potentially improved. This is a direct consequence of spreading, because even if the signal corresponding to a specific chip is obliterated by a deep frequency domain channel fade, after dispreading these effects are spread over the Walsh-Hadamard Transform (WHT) length. Hence there is a high chance of still recovering all the partially affected subcarrier symbols without errors. 3) As a test case, the OFDM-based 200 Mb/s MB-UWB network (IEEE 802.15.3a) are considered, but the simulation results are shown above section. 4) The simulation channel can be easily applied to NOS and NLOS situation with WHT transformation from Simulink model. The fading channels of UWB with low/high signal to noise ratio (SNR), multipath effects, and multiuser interference may introduce large errors in location. The location engine performs the following tasks: █ Data fusion techniques: Different data fusion techniques are implemented using Time Of Arrival (TOA), Angle Of Arrival (AOA), or a combination of both. █ Channel modeling: A multipath, multiuser channel environment is created that models path loss, shadowing, Rayleigh fading, and Doppler frequency effects. █ Parameter estimation: TOA and AOA estimation algorithms are implemented as part of the location finding engine. Different variations of algorithms are implemented for performance and comparison purposes. █ Configuring the physical layer for different wireless networks. Among the programmable parameters are spreading factor, packet size, training length, constellation type, modulation technique, carrier frequency, level of transmitted signal power, and the number of antennas at the transmitter for both sides. █ Configuring the mobile user conditions. The wireless channel models depend on the Doppler frequencies present in the environment. The Doppler frequency depends on the mobile speed and carrier frequencies as input and generates a Rayleigh fading channel with the U-shape Doppler spectrum. █ Configuring the environmental parameters and network geographical structure. One of the factors affecting the performance of the wireless location system is the environment type (e.g., bad urban, urban, suburban, or rural area). For example, in a bad urban area with many blocking objects and buildings, non-line of sight (NLOS) effects plays an important role in the estimation accuracy.

Process capability indices (PCIs) are widely used to assess whether an in-control process meets manufacturing specifications. In most applications of classical PCIs, the process characteristic is assumed normally distributed. However, the normal distribution has been found inappropriate in various applications. In the literature, the percentile-based PCIs are widely used to deal with the nonnormal process. One problem associated with the percentile-based PCIs is that they do not provide a quantitative interpretation to the process capability. In this study, new PCIs that have a consistent quantification to the process capability for both normal and nonnormal processes are proposed. The proposed PCIs are generalizations of the classical normal PCIs in the sense that they are the same as the classical PCIs when the process characteristic follows a normal distribution, and they offer the same interpretation to the process capability as the classical PCIs when the process characteristic is nonnormal. We then discuss nonparametric and parametric estimation of the proposed PCIs. The nonparametric estimator is based on the kernel density estimation and confidence limits are obtained by the nonparametric bootstrap, while the parametric estimator is based on the maximum likelihood estimation and confidence limits are constructed by the method of generalized pivots. The proposed methodologies are demonstrated using a real example from a manufacturing factory.

Two general classes of nonparametric kernel estimators of the hazard function are introduced, which include both a 1-parameter estimator and a more complex 3-parameter estimator. In addition, employing the idea of cross-validation, the authors present a data-based algorithm for smoothing parameter selection. The article compares the data-based 1and 3-parameter estimators in a simulation experiment to the maximum likelihood estimator assuming the correct failure distribution and censoring mechanism. The 3-parameter estimator is found to perform well over a wide range of settings. On the average, the estimator recovers the shape of the underlying failure hazard and is competitive with the parametric estimator over a subset of the positive half line. Two examples illustrate possible uses of the nonparametric estimators.

Sample covariances, estimated as mean-lagged products of random data, are poor and inaccurate fundaments for the non-parametric spectral estimation with tapered and windowed periodograms. However, the autocovariance can be estimated efficiently with a parametric method as transformation of an estimated time series model, if the model type and model order are known a-priori. A recent development in time-series analysis gives the possibility to automatically select the model type and the model order for data with unknown characteristics. After the computation of hundreds of candidate models of different orders and types, a statistical criterion can select a single time series model. The accuracy of this identification from many candidates is sufficient to approach the performance that can be obtained with parametric estimation if the type and the order of the time series model would be known a priori. Hence, the accuracy (mean square error) of parametric covariance estimates is typically the same or better than what can be achieved by non-parametric mean-lagged-product estimates.

Impact of loss aversion on the newsvendor game with product substitution

On the risk-averse procurement strategy under unreliable supply

Evaluation of the Schnabel, geometric and nonparametric estimators of population size was performed on a model population of 100 individuals which possessed a bivariate normal home range model with ox = 1 and a, = 2, a random spatial pattern, an average initial probability of capture of p = 0.10 or p = 0.40 and either a trap happy or trap shy learning process. Data were generated from a model which simulated 10-sample mark-recapture experiments consisting of 25 traps. Evaluation of these estimators reveals the magnitude of bias and variability present in such circumstances. The results indicate that the nonparametric estimator was the most robust under these conditions. J. WILDL. MANAGE. 43(2):474-483 Estimating the size of an animal population presents complex problems to population ecologists. General reviews of some of the methods were presented by Overton (1969) and Seber (1973). Estimators which have been developed are based on various assumptions, some of which are not fully satisfied in practice. When assumptions are not satisfied, wide variation may result in the estimates. Since many different estimators are available, it is desirable to evaluate their performance under varying degrees of violation of the assumptions. This would provide the investigator a measure of the degree of robustness of the estimators and shed light into which one would be most suitable for a specific problem. Field evaluation of the estimators is possible if mark-recapture experiments are performed in areas where the true sizes of the populations are known. However, this information is rarely available. An alternate approach for determining the robustness of the estimators is to develop simulation models to mimic populations exposed to mark-recapture experiments. In such models the parameters that control the animals' response to trapping can be varied, resulting in differential magnitudes of assumption violation. Recently, simulation has been used in the study of estimators of population parameters. Gates (1969) used computer simulation to evaluate the bias of a variety of line transect density estimators. Burnham and Overton (1969) and Manly (1970) employed computer simulation in evaluating the behavior of various markrecapture estimators. In another paper, Manly (1971) used simulation to examine Jolly's (1965) variance formulas for estimators of population parameters. In the present study, computer simulation techniques were also used. The objective of this work was to evaluate the sample expectation, variance, bias, and mean square error of mark-recapture estimators of population size when the assumption of equal probability of capture of animals is violated in response to a learning process related to the previous capture history. Appreciation is extended to the Division of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, and to the Department of Fisheries and Wildlife, Michigan State University, East Lan' Present address: Department of Fisheries and Wildlife, Michigan State University, East Lansing, MI 48824. 474 J. Wildl. Manage. 43(2):1979 This content downloaded from 157.55.39.80 on Fri, 22 Apr 2016 05:57:59 UTC All use subject to http://about.jstor.org/terms SIMULATION OF LEARNED TRAP RESPONSE *Zarnoch 475 sing, Michigan, for computer time used in the development of the model and evaluation of the estimators of population size. ESTIMATORS OF POPULATION SIZE Letting N = number of individuals in the population and S = number of samples taken, the following estimators were evaluated. Schnabel.-The Schnabel estimator, modified by Chapman (1952), is defined

For the characteristic of short storage life and quick value decay for Short Lifecycle Products (SLPs), it is supposed that suppliers provide Quantity Discount Pricing (QDP), lead time and demand rate comply with stochastic normal distributions, and stock-outs are permitted. And the optimal ordering models of SLPs were developed for discrete and continuous stochastic demand. Then the arguments analysis received the important reference results. In addition the algorithm procedure and numerical value example were provided to figure out the optimal order quantity and safe stock.

The impact of customer returns and bidirectional option contract on refund price and order decisions

In maximum likelihood estimation, the real but unknown innovation distribution is often replaced by a nonparametric estimate, and thus the estimation procedure becomes semiparametric. These semiparametric approaches generally involve two steps: the first step that incorporate an initial estimate of the model parameter to produce a residual sample, and the second step that uses the residuals to estimate the likelihood, which is subsequently maximized to obtain the final estimate of the model parameter. Therefore, the characteristics of the initial input estimator may be carried over to the final semiparametric estimator, and the performance of the semiparametric estimator will be impaired if the input estimate is deficient. In this article we have studied a onestep semiparametric estimator where no initial input is necessary. The estimation procedure is illustrated via a generalized autoregressive conditional heteroskedasticity (GARCH) model. Asymptotic properties of the estimator are established, and finite sample performance of the estimator is evaluated via simulation. The results suggest that the proposed one-step semiparametric estimator avoids significant drawbacks of its two-step counterparts. (JEL: C02, C22, C51)