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Mean integrated squared error

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22: 262: 144: 39: 288: 370: 86: 58: 65: 365: 105: 360: 72: 43: 54: 135: 314: 32: 79: 257:{\displaystyle \operatorname {E} \|f_{n}-f\|_{2}^{2}=\operatorname {E} \int (f_{n}(x)-f(x))^{2}\,dx} 281: 319: 127: 292: 354: 302: 21: 119: 131: 15: 147: 46:. Unsourced material may be challenged and removed. 256: 8: 174: 154: 247: 241: 207: 182: 177: 161: 146: 106:Learn how and when to remove this message 331: 291:random variables. Here, E denotes the 289:independent and identically distributed 7: 124:mean integrated squared error (MISE) 44:adding citations to reliable sources 339:Wand, M. P.; Jones, M. C. (1994). 191: 148: 14: 20: 55:"Mean integrated squared error" 31:needs additional citations for 238: 234: 228: 219: 213: 200: 1: 295:with respect to that sample. 371:Point estimation performance 315:Minimum distance estimation 280:is its estimate based on a 387: 298:The MISE is also known as 366:Nonparametric statistics 343:. CRC press. p. 15. 271:is the unknown density, 361:Estimation of densities 258: 259: 145: 40:improve this article 187: 136:probability density 320:Mean squared error 254: 173: 130:. The MISE of an 128:density estimation 116: 115: 108: 90: 378: 345: 344: 341:Kernel smoothing 336: 263: 261: 260: 255: 246: 245: 212: 211: 186: 181: 166: 165: 111: 104: 100: 97: 91: 89: 48: 24: 16: 386: 385: 381: 380: 379: 377: 376: 375: 351: 350: 349: 348: 338: 337: 333: 328: 311: 279: 237: 203: 157: 143: 142: 112: 101: 95: 92: 49: 47: 37: 25: 12: 11: 5: 384: 382: 374: 373: 368: 363: 353: 352: 347: 346: 330: 329: 327: 324: 323: 322: 317: 310: 307: 293:expected value 275: 265: 264: 253: 250: 244: 240: 236: 233: 230: 227: 224: 221: 218: 215: 210: 206: 202: 199: 196: 193: 190: 185: 180: 176: 172: 169: 164: 160: 156: 153: 150: 134:of an unknown 114: 113: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 383: 372: 369: 367: 364: 362: 359: 358: 356: 342: 335: 332: 325: 321: 318: 316: 313: 312: 308: 306: 304: 303:risk function 301: 296: 294: 290: 287: 283: 278: 274: 270: 251: 248: 242: 231: 225: 222: 216: 208: 204: 197: 194: 188: 183: 178: 170: 167: 162: 158: 151: 141: 140: 139: 137: 133: 129: 125: 121: 110: 107: 99: 96:February 2022 88: 85: 81: 78: 74: 71: 67: 64: 60: 57: –  56: 52: 51:Find sources: 45: 41: 35: 34: 29:This article 27: 23: 18: 17: 340: 334: 299: 297: 285: 276: 272: 268: 266: 138:is given by 123: 117: 102: 93: 83: 76: 69: 62: 50: 38:Please help 33:verification 30: 126:is used in 355:Categories 326:References 120:statistics 66:newspapers 223:− 198:∫ 195:⁡ 175:‖ 168:− 155:‖ 152:⁡ 309:See also 132:estimate 80:scholar 282:sample 267:where 122:, the 82:  75:  68:  61:  53:  87:JSTOR 73:books 59:news 284:of 118:In 42:by 357:: 305:. 300:L 286:n 277:n 273:ƒ 269:ƒ 252:x 249:d 243:2 239:) 235:) 232:x 229:( 226:f 220:) 217:x 214:( 209:n 205:f 201:( 192:E 189:= 184:2 179:2 171:f 163:n 159:f 149:E 109:) 103:( 98:) 94:( 84:· 77:· 70:· 63:· 36:.

Index


verification
improve this article
adding citations to reliable sources
"Mean integrated squared error"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
statistics
density estimation
estimate
probability density
sample
independent and identically distributed
expected value
risk function
Minimum distance estimation
Mean squared error
Categories
Estimation of densities
Nonparametric statistics
Point estimation performance

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