Prespecified Quantity Research Articles

A Reliable Cooperative Spectrum Sensing Strategy for Cognitive Radios

In cognitive radio networks (CRNs), the secondary users (SUs) need to continuously detect whether the primary users (PUs) occupy the spectrum. In order to improve the spectrum sensing accuracy, a novel reliable cooperative spectrum sensing strategy based on the detection results relayed twice from the secondary relays (SRs) to the secondary source (SS), referred to as CSS-DRT, is proposed in this paper. In this scheme, the spectrum sensing slot is divided into four equal sub-slots. In the first and third sub-slots, the SS and SRs detect the PU by themselves. Then, in the second sub-slot, if the SRs that detect the PU during the first sub-slot are more than or equal to a prespecified quantity, the corresponding SRs will send their flag signals (FSs) to the SS while the others keep quiet, where the FS is narrowband and indicates that the PU is present. Otherwise, if the SRs that detect the PU during the first sub-slot are less than the prespecified quantity, all the SRs will keep quiet in the second sub-slot. Meanwhile, the SS detects the PU based on the received signals from the PU and SRs. And, the SS uses the same method as employed in the second sub-slot to detect the PU in the last sub-slot wherein the SRs send their FSs based on their detections made during the third sub-slot. Finally, an ultimate decision is made by the OR ruler based on the SS detection results obtained during the spectrum sensing slot. Besides, we derive the closed-form expressions of the false alarm and detection probabilities for the proposed CSS-DRT scheme. In the end, simulation and numerical results show that our proposed scheme can achieve better performance than the non-cooperative method and an existing cooperative spectrum sensing method.

Dynamic lot sizing for a warm/cold process: Heuristics and insights

We consider the dynamic lot sizing problem for a warm/cold process where the process can be kept warm at a unit variable cost for the next period if more than a prespecified quantity has been produced. Exploiting the optimal production plan structures, we develop nine rule-based forward solution heuristics. Proposed heuristics are modified counterparts of the heuristics developed previously for the classical dynamic lot sizing problem. In a numerical study, we investigate the performance of the proposed heuristics and identify operating environment characteristics where each particular heuristic is the best or among the best. Moreover, for a warm/cold process setting, our numerical studies indicate that, when used on a rolling horizon basis, a heuristic may also perform better costwise than a solution obtained using a dynamic programming approach.

The cutoff transaction size and Gauss cost functions to the information value applying to the newsboy model

In this paper, two models are considered which differ in terms of information completeness. The first model involves the retailer having incomplete information regarding the state of customers demand. The second model involves the retailer having full information on the state of customers demand. Step function (here called Gauss function) can be applied such as the cost for mailing letters or packages in the post office and for shipping goods in containers. Therefore, the holding and penalty costs are represented by the Gauss functions to fit in with these practical situations. In addition, we assume that customers with an order larger than a prespecified quantity (here called cutoff transaction size) are still assumed to be satisfied in an alternative way, against additional cost. Moreover, when the maximum demand is large, much more time may be required to determine the optimal solution. Thus, we adopt and modify the algorithm of the Golden Section Search Technique to determine the optimal order-up-to level S and the cutoff transaction size q systematically and provide illustrative numerical example.

Linear Measurement Error Models with Restricted Sampling

The relationship between nutrient consumption and chronic disease risk is the focus of a large number of epidemiological studies where food frequency questionnaires (FFQ) and food records are commonly used to assess dietary intake. However, these self-assessment tools are known to involve substantial random error for most nutrients, and probably important systematic error as well. Study subject selection in dietary intervention studies is sometimes conducted in two stages. At the first stage, FFQ-measured dietary intakes are observed and at the second stage another instrument, such as a 4-day food record, is administered only to participants who have fulfilled a prespecified criterion that is based on the baseline FFQ-measured dietary intake (e.g., only those reporting percent energy intake from fat above a prespecified quantity). Performing analysis without adjusting for this truncated sample design and for the measurement error in the nutrient consumption assessments will usually provide biased estimates for the population parameters. In this work we provide a general statistical analysis technique for such data with the classical additive measurement error that corrects for the two sources of bias. The proposed technique is based on multiple imputation for longitudinal data. Results of a simulation study along with a sensitivity analysis are presented, showing the performance of the proposed method under a simple linear regression model.

A derivative-free optimization algorithm based on conditional moments

In this paper we propose a derivative-free optimization algorithm based on conditional moments for finding the maximizer of an objective function. The proposed algorithm does not require calculation or approximation of any order derivative of the objective function. The step size in iteration is determined adaptively according to the local geometrical feature of the objective function and a pre-specified quantity representing the desired precision. The theoretical properties including convergence of the method are presented. Numerical experiments comparing with the Newton, Quasi-Newton and trust region methods are given to illustrate the effectiveness of the algorithm.

Waiting for returns: using space–time duality to calibrate financial diffusions

Historically, tests of the Geometric Brownian Motion (GBM) model for security prices—and for that matter any diffusion process—have been performed by selecting a fixed interval of time (one day, one week, one month) t and then using the increments in logarithmic price ln1⁄2P over the predetermined t. Under the classical specification of the GBM model, the logarithmic price increments ln1⁄2P should be statistically independent from each other and these increments ln1⁄2P should be Normally distributed with a mean and variance that is proportional to the time increment t. This approach has a long tradition in finance. Research done in the 1950s by Kendall (1953) and Osborne (1959) as well as the work by Fama (1970) all the way through to the contemporary work of Campbell et al. (1997) based on Lo and MacKinlay (1988) focuses on a particular time interval t. Thus, for example, Kendall (1953) looked at a time increment of t 1⁄4 one week on the New York Stock Exchange, and concluded that the logarithmic price increments ln1⁄2P have a statistically insignificant serial correlation in addition to being (approximately) normally distributed. In another study, Fama (1970) looked at the 30 Dow Jones Industrial stocks with a t 1⁄4 one day, and concluded that there is a statistically significant positive serial correlation in logarithmic price increments ln1⁄2P . Poterba and Summers (1988) found that for a t 1⁄4 three years, the logarithmic price increments ln1⁄2P exhibit a statistically significant negative serial correlation which translates into a long-term mean reversion in prices. Among the many recent studies that document violations of the GBM by looking at the time series properties of returns to various financial instruments are Bakshi et al. (2000), Bollerslev et al. (1992), Cont (2001), Cont and da Fonseca (2002), and Nelson (1991). Nevertheless, the broad unifying methodology of this large literature is to select a time interval and then investigate price increments vis a vis that time interval. Hence, it is quite common to hear that the GBM-Lognormal model is rejected for hourly data while it is accepted for monthly data but rejected again for yearly data or some combination thereof. In fact, this was the recent conclusion of Levy and Duchin (2004). In this paper we propose an alternative way of thinking about the appropriate distribution. We investigate the GBM model for fixed ln1⁄2P intervals as opposed to fixed t intervals. In other words, we start at the beginning of a time series and judiciously select a price increment ln1⁄2P 1⁄4 d (for example, 1%) and then measure the amount of time 1 it takes the security to move the pre-specified quantity. After the security has moved by ln1⁄2P 1⁄4 d, we measure the time 2 at which the security moves an additional ln1⁄2P 1⁄4 d and so on and so forth. The final result is a collection of time increments ð iþ1 iÞ for each pre-specified ln1⁄2P . We then compare (statistically) the empirical distribution of the ð iþ1 iÞ’s to the theoretical distribution they should obey under the GBM model. If, indeed, the price increments are normal, then the ð iþ1 iÞ’s—for each particular ln1⁄2P —should obey the Inverse Gaussian (or Wald) distribution as a result of the Space–Time duality that exists for Brownian motion. We select an entire spectrum of ln1⁄2P ’s (for example, from 1% all the way to 15%) and then extract the appropriate sample of i’s (for each ln1⁄2P ) so as to measure goodness of fit and estimate confidence intervals for the implied drift and diffusion coefficients. Our approach should not be confused with, and is very different from, the paradigm of spectral *Corresponding author. Email: milevsky@yorku.ca

Admission control schemes to provide class-level QoS in multiservice networks

In this work, we consider the scenario where different classes of traffic with differing bandwidth requirements are to be supported over a link with finite capacity. The network will be required to meet class-level quality-of-service (QoS) constraints that are specified as relations between the call blocking probabilities of these traffic classes. The network will also be required to maintain maximum throughput performance. We develop two different admission control schemes that consider these two important criteria. First, we choose an objective that maximizes the throughput subject to the constraint that the maximum deviation from the desired class-level QoS is smaller than a certain pre-specified quantity. In the second approach, we choose an objective that minimizes the deviation from the desired class-level QoS subject to the throughput being greater than a pre-specified minimum value. We show how these problems can be converted to linear programming problems. We illustrate our schemes using numerical examples.

Flexible and Risk-Sharing Supply Contracts Under Price Uncertainty

We study supply contracts for deterministic demand but in an environment of uncertain prices. We develop valuation methodologies for different types of supply contracts. A “time-inflexible contract” requires the firm to specify not only how many units it will purchase, but also the timing of the purchase. A “time-flexible contract” allows the firm to specify the purchase amount over a given period of time without specifying the exact time of purchase. Other than time flexibility, the suppliers may offer “quantity flexibility” to the firm as well, i.e., purchase quantities could be within a prespecified quantity window. Finally, “risk-sharing” features can be incorporated in the contract in terms of the purchase price that the firm eventually pays to a supplier. Within a prespecified price window the firm pays the realized price, but outside of it the firm shares, in an agreed way, added costs or benefits. Given the structure of a supply contract, we study the firm's decision when to purchase and how many units in each purchase such that the expected net present value of the purchase cost plus inventory holding cost is minimized. We discuss optimal purchasing strategies for both time-flexible and time-inflexible contracts with risk-sharing features. Other interesting results include the analysis of two-supplier sourcing environments and the exploitation of quantity flexibility in such contracts. Our discussion illustrates how time flexibility, quantity flexibility, supplier selection, and risk sharing, when carefully exercised can effectively reduce the sourcing cost in environments of price uncertainty.

Estimation of the correlation between nutrient intake measures under restricted sampling.

Food frequency questionnaires (FFQs) are commonly used to assess dietary intake in epidemiologic research. To evaluate the FFQ reliability, the commonly used approach is to estimate the correlation coefficient between the data given in FFQ and those in food records (for example, 4-day food records [4DFR]) for nutrients of interest. However, in a dietary intervention study, a criterion for eligibility may be to select participants who have baseline FFQ-measured dietary intake of percent energy from fat above a prespecified quantity. Other instruments, such as the 4DFR, may be subsequently administrated only to eligible participants. Under these circumstances, analysis without adjusting for the restricted population will usually lead to biased estimation of correlation coefficients and other parameters of interest. In this paper, we apply likelihood-based and multiple imputation (MI) methods to accommodate such incomplete data obtained as a result of the study design. A simulation study is conducted to examine finite sample performance of various estimators. We note that both the MI estimate and the maximum likelihood (ML) estimate based on a bivariate-normal model are not sensitive to departures from this normality assumption. This led us to investigate robustness properties of the ML estimator analytically. We present some data analyses from a dietary assessment study from the Women's Health Initiative to illustrate the methods.

Similarity/equivalence trials for combination vaccines.

In a similarity or "equivalence" trial of a combination vaccine, we wish to show that the combination is sufficiently similar to the separately administered components in some measure of safety, immunogenicity, or efficacy to justify use of the combination. In this setting it is usually required to show similarity in one direction only; specifically, we design the trial to rule out superiority of the separate components by as much as a prespecified quantity theta 0 in an appropriate outcome measure (e.g., a difference or ratio). It is crucial that theta 0 be chosen to be clinically meaningful, so that any difference or ratio less than theta 0 is truly acceptable to clinicians. Estimation is generally more relevant than hypothesis testing in such a trial, and consequently it is natural to consider design and analysis in terms of confidence intervals. The same sample sizes can be obtained, however, from a hypothesis testing approach. The appropriate null hypothesis is that the separate components are superior to the combination by at least theta 0, with rejection of the hypothesis supporting a conclusion of similarity. It is not appropriate to design the trial to test the null hypothesis of no difference, as we would do if we wished to demonstrate superiority of the combination vaccine; failure to reject that hypothesis does not prove similarity, and we might reject the hypothesis when the true difference is unimportant clinically. Further, this inappropriate approach may result in a sample size either larger or smaller than necessary. Sample size formulations are available for various types of comparative measures, e.g., a difference of normally distributed means, a difference or ratio of proportions, and a ratio of hazards.

Sequential Confidence Regions in Inverse Regression Problems

In inverse regression problems (or more generally, the estimation of ratios of regression parameters) and errors-in-variables models, it has been shown by Gleser and Hwang that the length of any confidence interval with positive confidence level is infinite with positive probability. Therefore the confidence sets derived using asymptotic theory, although having correct asymptotic coverage probability, typically have zero confidence level when the sample size is fixed. Is it possible to construct a sequential confidence interval with finite length and $1 - \alpha > 0$ confidence level? The answer is no for any finite stage sequential sampling. The answer is, however, yes for a fully sequential scheme, as demonstrated by Hwang and Liu. For the inverse regression problem, and more generally the set estimation of a ratio of regression parameters, we construct a $(1 - \alpha)$ confidence sequence. Applying such a confidence sequence, we can construct a $(1 - \alpha)$ sequential confidence interval with the length less than a prespecified quantity.

A Visually Weighted Quantization Scheme for Image Bandwidth Compression at Low Data Rates

Source encoding of images for bandwidth compression has become attractive in recent years because of decreasing hardware costs. By combining the source encoding approach with transform coding techniques, it is possible to obtain good image quality at low data rates. The general aspects of such a system are presented. The design of the quantizer for transform coefficients, which is the major source of error associated with the compression process, is considered using a visual fidelity criterion and subject to the constraint that the entropy of the quantizer be a prespecified quantity. A visually weighted suboptimal quantization scheme is developed to take into account the relative importance of different transform coefficients to the human visual system.