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7,0 6,5 3,0 6,5 6,5 1,5 1,2 9 6,5 7,0 3,0 6,5 6,5 6,5 6,5 7,5 4,0 6,5 6,5 1,0 0,5 10 4,0 6,5 6,5 4,0 7,5 7,0 7,0 7,5 3,0 6,5 6,5 1,4 1,3 11 7,5 7,0 3,0 7,5 7,0 7,5 7,0 4,0 7,5 6,5 7,0 1,2 1,1 12 7,5 6,5 3,0 6,5 4,0 3,0 7,5 6,5 4,0 6,5 6,5 1,6 1,5 13 7,5 6,5 6,5 6,5 4,0 7,5 4,0 6,5 7,5 6,5 6,5 0,9 0,7 14 6,5 3,0 6,5 7,0 7,0 7,0 7,0 7,0 7,0 6,5 7,0 0,7 0,6 15 7,5 7,0 6,5 7,5 7,5 6,5 7,0 3,0 7,5 7,5 7,3 0,9 0,8 Desvio padrão 0,3 0,4 0,4 Portanto, as estimativas de bootstrap dos parâmetros de interesse são dadas por: ; ; �PAGE � Cap.11 – Pág.� PAGE �1� _1069062100.unknown _1069100586.unknown _1069109023.unknown _1069137877.unknown _1069139553.unknown _1069192006.unknown _1069193684.unknown _1069193956.unknown _1069194541.unknown _1069194619.unknown _1069198886.unknown _1069198907.unknown _1069198834.unknown _1069194593.unknown _1069194137.unknown _1069193881.unknown _1069193917.unknown _1069193857.unknown _1069193122.unknown _1069193212.unknown _1069193385.unknown _1069193171.unknown _1069192230.unknown _1069193101.unknown _1069192139.unknown _1069190420.unknown _1069191516.unknown _1069191866.unknown _1069191904.unknown _1069191538.unknown _1069190622.unknown _1069191463.unknown _1069189524.unknown _1069190263.unknown _1069190276.unknown _1069190403.unknown _1069189578.unknown _1069139627.unknown _1069189305.unknown _1069139618.unknown _1069139180.unknown _1069139369.unknown _1069139446.unknown _1069139234.unknown _1069138576.unknown _1069138720.unknown _1069138141.unknown _1069138051.unknown _1069138119.unknown _1069136773.unknown _1069137273.unknown _1069137620.unknown _1069137784.unknown _1069137288.unknown _1069137245.unknown _1069137261.unknown _1069136880.unknown _1069137212.unknown _1069109555.unknown _1069110402.unknown _1069110442.unknown _1069109769.unknown _1069110024.unknown _1069109085.unknown _1069109431.unknown _1069109033.unknown _1069104586.unknown _1069107746.unknown _1069107997.unknown _1069108288.unknown _1069108579.unknown _1069108180.unknown _1069107886.unknown _1069107988.unknown _1069107801.unknown _1069106288.unknown _1069107044.unknown _1069107686.unknown _1069106348.unknown _1069105283.unknown _1069105864.unknown _1069105181.unknown _1069102225.unknown _1069103680.unknown _1069103920.unknown _1069104455.unknown _1069103898.unknown _1069102613.unknown _1069103301.unknown _1069102451.unknown _1069101144.unknown _1069101810.unknown _1069102095.unknown _1069101802.unknown _1069100982.unknown _1069101060.unknown _1069100705.unknown _1069069703.unknown _1069073062.unknown _1069097040.unknown _1069099923.unknown _1069100235.unknown _1069099707.unknown _1069073595.unknown _1069073642.unknown _1069073398.unknown _1069073516.unknown _1069072405.unknown _1069072878.unknown _1069072884.unknown _1069072587.unknown _1069070952.unknown _1069072113.unknown _1069072254.unknown _1069072091.unknown _1069070377.unknown _1069068217.unknown _1069068829.unknown _1069068944.unknown _1069069311.unknown _1069068927.unknown _1069068739.unknown _1069068814.unknown _1069068706.unknown _1069063321.unknown _1069068029.unknown _1069063352.unknown _1069063421.unknown _1069062281.unknown _1069063261.unknown _1069063061.unknown _1069062127.unknown _1056482761.unknown _1069057346.unknown _1069058698.unknown _1069059270.xls Gráf1 0.00512 0.02304 0.03456 0.02048 p L(p) 11.1 Distribuição amostral de p^ # sucessos 0 1 2 3 4 5 p^ 0.0 0.2 0.4 0.6 0.8 1.0 P(p^) 0.3277 0.4096 0.2048 0.0512 0.0064 0.0003 E(p^) = 0.2 Var(p^) = 0.032 11.2 Var(p^) <= 1/(4n) n 10 25 100 400 Limite superior de Var(p^) 0.025 0.01 0.0025 0.000625 11.2 Limite superior de Var(p^) n Limite superior de Var(p^) 11.5 Estimadores t1 t2 Resultados da simulação Média 102 100 Variância 5 10 Mediana 100 100 Moda 98 100 Propriedades dos estimadores Viés 2 0 Variância 5 10 EQM 9 10 11.6 a) mi 6 7 8 9 10 t yt (yt-mi)^2 (yt-mi)^2 (yt-mi)^2 (yt-mi)^2 (yt-mi)^2 1 3 9 16 25 36 49 2 5 1 4 9 16 25 3 6 0 1 4 9 16 4 8 4 1 0 1 4 5 16 100 81 64 49 36 S(mi) 114 103 102 111 130 S(mi) parece ser mínimo para mi aproximadamente igual a 7,5. (b) ybarra = 7.6 11.6 Xbarra % Histograma de Xbarra 11.7 mi S(mi) 11.9 Ano (t) 1967 1969 1971 1973 1975 1977 1979 Inflação (yt) 128 192 277 373 613 1236 2639 a) b) tbarra = 1973.00 ybarra = 779.71 soma(t*yt) = 10788548.00 soma(t^2) = 27249215.00 Estimativas de mínimos quadrados de alfa e beta alfa^ = -350026.73 beta^ = 177.80 c) y(1981) = 2202.143 d) Sim, pois o gráfico mostra que a inflação cresceu exponencialmente no período observado. 11.9 Inflação (yt) Ano (t) Inflação (yt) 11.10 t 1 2 3 4 5 6 7 8 9 10 xt 1.5 1.8 1.6 2.5 4.0 3.8 4.5 5.1 6.5 6.0 yt 66.8 67.0 66.9 67.6 68.9 68.7 69.3 69.8 71.0 70.6 xbarra = 3.73 ybarra = 68.66 soma(xt*yt) = 2586.43 soma(xt^2) = 169.25 Estimativas de mínimos quadrados de alfa e beta alfa^ = 65.513 beta^ = 0.844 11.11 n = 5 x = 3 Função de verossimilhança da distribuição Binomial(5;p) p 0 1/5 0 2/5 0 3/5 0 4/5 L(p) 0.005 0.023 0.035 0.020 11.11 p L(p) 11.14 11.15 Intervalo de confiança Média amostral Tamanho da amostra Desvio padrão da população Coeficiente de confiança Limite inferior Limite superior 170 100 15 95% 167.06 172.94 165 184 30 85% 161.82 168.18 180 225 30 70% 177.93 182.07 11.16 a) Intervalo de confiança xbarra n s Coef. confiança Limite inferior Limite superior 800 400 100 99% 787.06 812.94 b) erro n s zgama 0.98 400 100 ? zgama = erro*raiz(n)/s => zgama = 0.196 => gama = 15.54% c) erro n s zgama 7.84 ? 100 1.96 n = (s*zgama/erro)^2 => n = 625 11.16 S^2 % Distribuição de S^2 11.17 t % Histograma de t 11.18 a) erro n s zgama 1 ? 10 1.96 n = (s*zgama/erro)^2 => n = 384.14 n aprox. = 385 b) erro n s zgama 1 ? 10 2.58 n = (s*zgama/erro)^2 => n = 663.49 n aprox. = 664 11.19 a) erro n sigma zgama 1 ? 10 1.75 n = (sigma*zgama/erro)^2 => n = 306.49 n aprox. = 307 b) Intervalo de confiança xbarra n sigma Coef. confiança Limite inferior Limite superior 50 307 10 92% 49.00 51.00 11.20 Intervalo de confiança Intervalo de confiança conservador p^ n Coef. confiança Limite
