Statistics is a mathematical science for collecting, analyzing, interpreting and drawing conclusions from a set of data. The first instance of descriptive statistics was given by the “bills of mortality” collected by John Graunt’s in 1662. Around 1749, the meaning of statistics was limited to information about “states” to design the systematic collection of demographic and economic data. In the early 19th century, accumulation of information intensified, and the definition of statistics extended to include disciplines concerned with the biology and the biomedicine. The main important areas of statistics are the descriptive statistics and the inferential statistics. The first statistical method gives numerical and graphic procedures to summarise a collection of data in a clear and understandable way without assuming any underlying structure for such data, the second one provides procedures to draw inferences about a population on the basis of observations obtained from samples. Therefore, the use of descriptive and inferential methods enables researchers to summarize findings and conduct hypothesis testing. The descriptive statistics is the primary step in any applied scientific investigation to simplify large amounts of data in a sensible way. Indeed, the goal of descriptive statistics is to give a clear explanation and interpretation of the information collected during an experiment. For instance, in medicine and biology, the observations obtained by a phenomenon are large in number, dispersed, variable and heterogeneous preventing the researcher from directly understanding it. To have a full knowledge of the under investigated phenomenon, it is first necessary to arrange, describe, summarize and visualize the collected data (Spriestersbach et al., 2009). In this article, we present two statistical descriptive methods: graphical and numerical. The graphs and tables are used to organize and visualize the collected data. Numerical values are computed to summarize the data. Such numbers are called parameters if they describe population; they are called statistics if they describe a sample. The most useful numerical value or statistics for describing a set of observations are the measures of location, dispersion and symmetry. Generally, graphical methods are better suited than numerical methods for identifying patterns in the data, although the numerical approaches are more precise and objective. Since the numerical and graphical approaches complement each other, it is wise to use both. In the following sections, we first introduce the statistical data types (quantitative or qualitative), and then, the way to organize and visualize collected data using tables and graphs. Several kinds of statistics measures (location, dispersion and symmetry) are also discussed to provide a numerical summary of data (Manikandan, 2011a,b,c; Wilcox and Keselman, 2003). Finally, clinical data are elaborated and discussed as an illustrative example.

Classification images have become popular tools in psychophysics, yet difficulties associated with their interpretation have often hindered their application. Alternative methods for characterizing perceptual filters have been proposed, and the discussion has often focussed on the degree to which classification images are optimal statistical estimators of system components (e.g. kernels). This technical note argues that those difficulties become irrelevant once the tool is situated within a data-driven interpretational framework. Within this framework, classification images and their nonlinear derivatives are understood not as transparent estimates of system components, but instead as transparent descriptors of data structure. The many pitfalls associated with the former approach, and the power of the latter, are demonstrated via combination of counter-intuitive computer simulations with empirical examples from published literature. A change in perspective over the manner in which this tool is understood and utilized may lead to a more productive engagement with this methodology.

Introduction

What is a classification image, and why is it useful?

We constantly ‘filter’ the world around us. Our sensors (eyes, ears, nose, tongue, skin) are bombarded by signals of various kinds, and our ability to discriminate between two such signals (e.g. blue versus red colours) relies on perceptual filters that retain one signal and throw out the other. Our brain then exploits the activity of many such filters to perform specific actions for the purpose of successfully interacting with the environment. In its simplest account, this filtering process can be summarized by a trace (bellshaped curve in Fig. 1A) that records the response of the perceptual filter (plotted on the y axis) to different values of an environmental characteristic, such as the position of an object along the horizon (plotted on the x axis). From Fig. 1A we infer that this specific filter is selective for objects sufficiently close to the middle position long the x axis (stimulus in Fig. 1C), but stops responding when the object is moved further away from the midpoint (Fig. 1D). The filtering stage outlined above returns a continuous value. Our behavioural decisions, however, do not come in this format: we either decide to run away from a predator, or stay put; we either eat a potentially poisonous food item, or we drop it. In other words, most decisions we take on how we use our sensory representation to interact with the world are discrete (typically binary): we either choose to take an action, or we choose not to. How do we go from our perceptual representation, which comes in the form ‘it is 2× more likely that a predator is hiding behind that bush than not’, to the decision ‘run away!’? The simplest model of how this conversion may happen involves a threshold (Green & Swets, 1966): if the ratio between the likelihood of ‘predator’ versus ‘non-predator’ is greater than some value, e.g. 1, we run away; if it is smaller than that value, we stay put. Because we tend to produce this kind of response somewhat erratically, i.e. our estimate of the likelihood is not always identical under the same environmental conditions due to noise in our sensors and our decisional process (Green, 1964; Neri, 2010a), any model of what decision we take must be itself probabilistic: it can only predict that we will run with probability x. To this end, the model in Fig. 1A converts the output from the filter (on the y axis) onto the probability that it will lead to one of two binary choices (e.g. ‘yes’ versus ‘no’). The ‘link’ function is called a static nonlinearity (an example is shown in Fig. 1B). This function is necessary if one is to re-format the output of the filtering stage into the currency of real-world actions

In recent years cities are in search for new ways to promote themselves. Due to fast changes in technology and the shift from local to a globalized environment, cities are forced to compete with each other in order to be an attractive tourist destination, workplace, cultural rich place and much more (Kotler, 2002). Kavaratzis argues that the rising competition among cities might be seen as one of the effects of the globalization, which is visible in various forms and activity fields (Kavaratzis, 2005, p. 1). The contemporary city has to be up dated continuously. In that sense cities develop strategies to support, to `sell` and advertise them within the global market. Literature survey reveals that there are mainly three approaches for promoting cities: cultural mega events, restoration and promoting heritage and the construction of iconic buildings (Hankinson, 2006, p.240; Kavaratzis, 2005, p.1). Among these approaches, construction of iconic buildings has been extensively utilized by many cities in order to get attention and attraction. The main motive behind this attempt is to create an identifiable image. It should also be noted that the restless competition between cities is strongly related to the concept of Quality of Life (QOL), which can briefly be defined as: ‘Quality of Life is a feeling of well-being, fulfilment, or satisfaction on the part of residents or visitors to a place’ (Andrews, 2001, p.202). Existing studies (Bigne´ et al., 2001; Petrick; Chen et al.; Chi et al.) confirm a positive relationship between image and satisfaction of visitors/tourists. A strong and identifiable image would have a positive impact on the satisfaction of the visitors. Since iconic buildings have a great contribution to the identifiable image of a city or place (Jencks, 2005, p.185), it can be suggested that they can indirectly influence the feeling of well-being and satisfaction of residents and visitors, thus there is a relationship between the image of place and QOL. Accordingly, this paper aims to question the influence of iconic architecture through creating identifiable images on Quality of life. In order to justify the relationship between the image of the city and QOL, the paper firstly, puts forward very briefly the concepts of City Identity and Branding with an emphasis on the city image, which is limited to the contribution of iconic buildings. Secondly, the paper discusses the contribution of iconic buildings through their meaning in terms of the image of the city to QOL.

Despite Brazil’s progress in labor market outcomes over the last decade, labor market outcomes of youth – particularly those from disadvantaged socio-economic contexts – continue to be markedly worse than almost any other demographic group. Youth face lower wages, higher levels of informality, and more frequent unemployment spells. Their attachment to the labor market is also tenuous and irregular, with frequent entry and exit. This paper analyzes an innovative approach at dealing with unemployment among disadvantaged youth living in Rio de Janeiro’s slums (or favelas), pioneered by a small NGO, Galpão Aplauso. The novel dimension of this program is the use of expressive arts and theatre as a pedagogical tool. This tool is used as part of a training program that also includes vocational and academic training, as well as training in work-readiness skills. We expect that the bundle offered by Galpão may impact employment through a number of channels. First, it can teach specific academic and vocational skills which employers demand. These are basic numeracy, reading, as well as specific skills required by certain trades. Second, it can teach specific conducts required to work in a formal job environment. These work-readiness skills are conducts that employers expect from the workforce, but that youth in the marginalized communities in Rio’s favelas often lack. Beyond the specific technical or work-readiness skills, the program can build broader cognitive and socio-emotional skills (sometimes referred to as non-cognitive skills) that are known to be important for labor market outcomes. The economics and psychology literature shows that socio-emotional skills do change over the life-cycle and can me molded, particularly at younger ages. However, whereas specific work-readiness skills may be easier to change, we are more ambivalent regarding the ability of youth-training programs to impact broader types of socio-emotional skills for youth and young adults. Program participants could see higher labor market outcomes due to formation of vocational, academic, and socio-emotional skills. Using standard labor market participation questions, we can test the program’s overall impact on employment and earnings. We can also test the program’s impact on broad socio-emotional skills measured by standard psychological tests. However, we cannot parse out what share of the program impacts is due to higher vocational skills, higher academic skills, or higher socio-emotional skills, as the experiment was not designed with separate treatment arms that would allow for separate estimation of these different channels.

مقاله سال 2016

Unlike soccer, American football and tennis, relatively little work has been published on forecasting in cricket. This seems especially strange given that there are known to be huge betting markets for cricket. The work that has been done on forecasting in cricket has largely been concerned with pre-match forecasting. However, in recent times, the growth in the popularity of in-play betting in all sports, where punters place bets during a game (or match), has meant that models that enable forecasts to be made as the game progresses are in high demand. Cricket is a sport that lends itself particularly to in-play betting: unlike soccer, for example, the discrete nature of the game means that bookmakers and punters alike have ample opportunities tobe active in markets during the game, and as such, cricket attracts extremely large in-play betting volumes. For example, the total amount bet during a typical major OneDay International (ODI) involving Pakistan or India is in the order of $1bn (according to a personal communication from a betting industry insider in 2013). In this paper, we present an in-play forecasting model for One-Day International cricket, and use the model to estimate the probability of victory for a team at any moment during a game.

Of course, betting is not the only use of a forecasting model. A forecasting model like that presented here could be used for several purposes. Team coaches may use in-play forecasting probabilities to assess the merits of various different strategies or to analyse player and team performances. In addition, the media could use the model to identify key moments in a match and enhance the television coverage further.

Previous work in One-day International (ODI) cricket has focussed largely on the problem of resetting targets in limited overs cricket following interruptions to play.

مقاله سال 2016

Consider the case where an analyst has two competing one-step-ahead forecasts for a time series variable yt , namely yˆ1,t and yˆ2,t , for a sample t = 1, 2, . . . , T . The forecasts have the associated forecast errors εˆ1,t and εˆ2,t , respectively. To examine which of the two sets of forecasts provides the best accuracy, the analyst can use criteria based on some average or median of loss functions of the forecast errors. Well-known examples include the root mean squared error (RMSE) and the median absolute error (MAE); see Hyndman and Koehler (2006) for an exhaustive list of criteria, and also Table 1.

t of criteria, and also Table 1. As there is always one set of forecasts that scores lower on some criterion, it seems wise to test whether any observed differences in forecast performances are statistically significant. To test statistically whether the obtained values of these criteria are equal, the analyst can rely on the methodology proposed by Diebold and Mariano (1995) (DM); see also Diebold (2015) for a recent review. This methodology is based on the loss functions li,t = f(yt, yˆi,t) for i = 1, 2. Denoting the sample mean loss differential by d¯ 12, that is, d¯ 12 = 1 T T 1 (l1,t − l2,t), and a consistentestimate of the standard deviation of d¯ 12 by σˆd¯ 12 , the DM test for one-step-ahead forecasts is DM = d¯ 12 σˆd¯ 12 ∼ N(0, 1),

under the null hypothesis of equal forecast accuracy. Even though Diebold and Mariano (1995, p. 254) claim that this result holds for any arbitrary function f , it is quite clear that the function should allow for proper moment conditions in order to yield the asymptotic normality of the test. In fact, as will be argued in Section 2 below, many of the functions that are commonly applied in the forecast literature fail to qualify as useful functions for the DM methodology. This note continues with a brief summary of typical functions in Section 2, along with a concise discussion of which of these functions are useful in the DM framework. It is found that the absolute scaled error (ASE) recommended by Hyndman and Koehler (2006) does have the favorable properties, while various other criteria do not. Section 3 reports on limited simulation experiments which support these insights. The main conclusion of this note is to confirm that the use of the Mean ASE (MASE) criterion is recommended.

مقاله سال 2016

The question of finding weights for combining density forecasts is non-trivial, and is currently being debated in the forecast combination literature. The latest work in this area is by Kapetanios, Mitchell, Price, and Fawcett (2015), and examples of early contributions are provided by Tay and Wallis (2000)and Corradi and Swanson (2006). The reader is also invited to peruse the review by Timmermann (2006) for a thorough review of the forecast combination literature.

In a recent paper, Hall and Mitchell (2007) propose a practical way of obtaining weights in a linear combination of density forecasts. The weights are found by maximizing the average logarithmic score of the combined density forecast. Hall and Mitchell (2007) call these weights ‘‘optimal’’ because they minimize the ‘‘distance’’ between the forecast and true (but unknown) densities, as measured by the Kullback–Leibler Information Criterion (KLIC).

Although Hall and Mitchell(2007) show how these weights can be used, the paper does not detail the theoretical properties of the estimators of the weights. The motivation for the study relies on asymptotic theory, namely that the number of time periods grows to infinity (T → ∞). Geweke and Amisano (2011) propose an approach that is similar to that of Hall and Mitchell (2007) using Bayesian methods, and provide a theoretical justification for the use of optimal linear combinations.

The time variation in second and higher-order moments is an important phenomenon for assessing (tail) risk, constructing hedge strategies, and pricing assets. Exponentially weighted moving average (EWMA) methods have proved to be useful tools for capturing such time variation in a parsimonious and effective way. Here, we develop a new empirical methodology that extends and improves upon the standard EWMA approach. Our framework uses the higher-moment properties of the forecasting distribution to drive the dynamics of volatilities and other timevarying parameters. This ensures that the new method is robust to outliers if a non-normal forecasting distribution is used, as is typically the case when forecasting financialasset returns. The new method is easy to implement and remains similar in spirit to the highly familiar EWMA approach of RiskMetricsTM.

The score-driven EWMA (SD-EWMA) model that we propose builds on a new observation-driven methodology, namely the generalized autoregressive score (GAS) dynamics; see Creal, Koopman, and Lucas (2011, 2013) and Harvey (2013). In particular, we consider an integrated version of the score-driven dynamics. The analogy is simple: just as the standard EWMA approach is a special case of the IGARCH(1,1) model of Bollerslev (1986) and Engle (1982), the proposed SD-EWMA approach is a special case of the IGAS(1,1) model of Creal et al. (2013). Its key feature is the fact that the time-varying parameter dynamics are driven by the score of the forecasting distribution. Empirical evidence of the usefulness of score-driven dynamics is provided by Creal, Schwaab, Koopman, and Lucas (2014), Harvey and Luati (2014), and Lucas, Schwaab, and Zhang (2014), for example, while Blasques, Koopman, and Lucas (2015) demonstrate the information-theoretic optimality properties of score-driven updates.

The intuition for using the score is straightforward. As an example, consider forecasting a time-varying variance of a fat-tailed distribution. If one uses the standard EWMA approach, a large absolute return has a major impact on the next period’s estimated variance, due to the use of squared returns in the variance updating equation. Given the integrated nature of the EWMA dynamics, this impact affects a large number of the subsequent volatility estimates. If one accounts for the fat-tailedness of the return distribution by using a score-driven propagation mechanism for the variances, the impact of incidental tail observations is reduced substantially. This mitigation or robustifying mechanism is particularly important in our current context with integrated (infinite memory) dynamics.

مقاله سال 2016

When several forecasts of the same event are available, it is natural to try and find a (linear) combination of these forecasts that is the ‘best’ in some sense. If we define ‘best’ in terms of the mean squared error and the variances and covariances of the forecasts are known, then optimal weights can be derived. In practice, though, these (co)variances are not known and need to be estimated. This leads to estimated optimal weights and an estimated optimal forecast combination. Empirical evidence and extensive simulations show that the estimated optimal forecast combination typically does not perform well, and that thearithmetic mean often performs better. This empirical fact has become known as the ‘forecast combination puzzle’. The history of the puzzle is elegantly summarized by Graefe, Armstrong, Jones, and Cuzán (2014, Section 4), and Smith and Wallis (2009) made a rigorous attempt to explain it, using simulations and an empirical example. They showed that the effect of the error on the estimation of the weights can be large, thus providing an empirical explanation of the forecast puzzle. Smith and Wallis (2009) use the words ‘finite-sample’ error, which suggests that this error may vanish asymptotically. However, it is not so easy to find an asymptotic justification for ignoring the noise generated by estimating the weights. To begin with, it is not clear what ‘asymptotic’ means here. What goes to infinity? The number of forecasts? If so, then the number of weights also goes to infinity. The number of observations underlying the total (but finite) set of forecasts? That would make more sense, but it would be difficult to analyze.

In this paper, we provide a theoretical explanation for the empirical and simulation results of Smith and Wallis (2009) and others. The key ingredient of our approach is the specific acknowledgement that the optimal weights should be derived by taking the estimation step into account explicitly. In other words, we view the derivation and estimation of optimal weights as a joint effort, not as two separate efforts. This approach differs from (almost) all previous research, not only the study by Bates and Granger (1969), but also later contributions, important and insightful though they may be, such as those of Elliott (2011), Hansen (2008), Hsiao and Wan (2014), and Liang, Zou, Wan, and Zhang (2011). The separation of the mathematical derivation and statistical estimation can be quite dangerous. However, even though the disadvantages of such separations have been highlighted, they are still quite common in econometrics, and specifically in the modelaveraging literature, which explicitly attempts to combine model selection and estimation, so that uncertainty in the model selection procedure is not ignored when reporting properties of the estimates; see for example Magnus and De Luca (2016).