Applied Nonparametric Regression

Härdle, Wolfgang Karl

doi:10.1017/ccol0521382483

Cited by 1,712 publications

(356 citation statements)

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“…8 These four observations correspond to United Arab Emirates (1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970), Djibouti (1970Djibouti ( -1980, Mozambique (1970Mozambique ( -1980 and Somalia (1970Somalia ( -1980. 9 Although clusters of countries are detected that differ from the trend, both in mean and in variance (although we cannot reject to be equal to one).…”

Section: 2-gibrat's Lawmentioning

confidence: 77%

“…First, the estimated kernel of the mean is close to zero. However, the trend is slightly decreasing; the bigger the size, the smaller the growth rate 9 . But the null hypothesis of this mean being equal to zero can be rejected at a 5 % significance level only for some values in the upper tail, so, except for these values of the distribution, Gibrat's law holds in the period examined.…”

Section: 2-gibrat's Lawmentioning

confidence: 97%

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Zipf’s and Gibrat’s laws for migrations

2010

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This paper analyses the evolution of the size distribution of the stock of emigrants in the period 1960-2000. Has the distribution of the stock of emigrants changed or has there been some convergence? This is the question discussed in this work. In particular, we are interested in testing the fulfillment of two empirical regularities studied in urban economics: Zipf's law, which postulates that the product between the rank and size of a population is constant; and Gibrat's law, witch states that growth rate of a variable is independent of its initial size. We use parametric and non-parametric methods and apply them to absolute (stock of emigrants) and relative (migration density, defined as the quotient between the stock of emigrants of a country and its total population) measurements.

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Section: 2-gibrat's Lawmentioning

confidence: 77%

Section: 2-gibrat's Lawmentioning

confidence: 97%

Zipf’s and Gibrat’s laws for migrations

2010

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“…Several methods for choosing the bandwidth exist and are discussed in Silverman [25], Härdle [26] and Scott [27]. The method discussed by Silverman was used in this study and a bandwidth of 0.9 σn −1/5 selected, where σ is the standard deviation of the data and n is the number of data points.…”

Section: Bandwidthmentioning

confidence: 99%

Relating Background NO2 Concentrations in Air to Air Mass History Using Non-Parametric Regression Methods: Application at Two Background Sites in Ireland

Donnelly

Broderick

Misstear

2011

Environ Model Assess

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The concentration of nitrogen dioxide (NO 2 ) in background air varies temporally and spatially and is influenced by meteorological and anthropogenic factors. Background concentrations used in local air quality modelling studies have a significant effect on the accuracy of the overall result and when based on short-term monitoring data, variation in concentrations with air mass history is often unaccounted for. The current paper presents a powerful tool for the quantification and separation of local and regional air mass effects on background air quality. The origin of and the regions traversed by an air mass prior to reaching a receptor has been modelled using HYsplit-4. Trajectories (between 12 and 96 h duration) were defined based on the frequency with which they passed into 16 predefined compass quadrants and each represented as a vector. Using this vector as the predictor variable and the background concentration as the response variable, non-parametric regression using a Gaussian kernel function was carried out. A graphical output indicated the trajectory direction of maximum NO 2 concentration, while allowing distinction to be made between spurious and true peaks. In all cases, air mass history was found to have a statistically significant effect on NO 2 concentrations. Incorporating emissions data into the analysis local and regional effects were separated and quantified. It was found that emissions in the UK and Europe have a significant effect on background NO 2 concentrations in Ireland and in some instances supersede domestic emissions. The methods can be used to identify source regions, separate local and regional effects and improve predictions of background concentrations based on limited monitoring data. In particular, the results highlight the importance of considering air mass history when assessing background concentration levels for use in local air quality modelling studies.

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“…It can be seen that the optimal value of h n1 is smaller than the optimal value of h n2 in all cases. When n is larger, both h n1 and h n2 need to be smaller and both nh n1 and nh n2 need to be larger, which is often true for local smoothing procedures (Härdle 1990). When σ is larger, both h n1 and h n2 need to be chosen larger, which is intuitively reasonable.…”

Section: Numerical Studymentioning

confidence: 99%

“…Conventional local smoothing procedures, including running averages (Tukey 1977), locally weighted scatter plot smoothing (Cleveland 1979), kernel smoothing (Härdle 1990), local polynomial kernel smoothing (Fan and Gijbels 1996), and several others, are appropriate for estimating continuous regression functions. When the underlying regression function has jumps, the estimated functions by conventional procedures are not statistically consistent at the jump positions.…”

Section: Introductionmentioning

confidence: 99%